Methods for extending a range for assigning attributes to an object in an image

ABSTRACT

There is provided a method for assigning an attribute to x-ray attenuation including the steps of acquiring first and second reference material equivalent path length information associated with a first range of dual-energy x-ray attenuation information, acquiring second and third reference material equivalent path length information associated with a second range of dual-energy x-ray attenuation information, and, joining the first the first dual-energy x-ray attenuation information range with the second dual-energy x-ray attenuation information range using coefficients representing dual-energy x-ray attenuation information of the second reference material to define a third dual-energy x-ray attenuation information range upon which may be imposed dual-energy x-ray attenuation values within the third dual-energy x-ray attenuation information range to determine corresponding first reference material equivalent path lengths and third reference material equivalent path lengths.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is a non-provisional of and claims priority toand the benefit of U.S. Provisional Patent Application No. 62/615,120,filed on Jan. 9, 2018, entitled “METHODS AND APPARATUS FOR DETERMININGAND ANALYZING THE PROPERTIES OF AN OBJECT SCANNED WITH IONIZINGELECTROMAGNETIC RADIATION”, which is incorporated by reference in itsentirety.

BACKGROUND

The present invention relates to x-ray scanning of objects. Moreparticularly, the present invention relates to x-ray scanning of objectsfor determining the properties of the materials of which the objects arecomposed.

There are presently many methods and apparatus for scanning objects andmaterials using electromagnetic radiation, such as x-rays, for thepurpose of identifying the material of which the object being scanned ismade. Although certain techniques are useful in basic medical imagingapplications, such techniques usually do not provide a continuousdiscrimination of materials over a wide range of atomic compositionrequired for identifying materials for security screening, whichinvolves identifying materials which may pose a threat. Moreover,security screening of objects is often used at locations with highthroughput, such as airports, where people and baggage must be scannedat a relatively high rate so as to avoid congestion at securitycheckpoints.

Liquid, aerosol or gel (LAG) materials are of particular concern becausethey can be stored in small containers that are often carried bypassengers, such as drinking bottles, and may potentially be composed ofan explosive material. Moreover, non-explosive LAG materials,particularly liquids, may be stored in separate containers and maypotentially be later combined to make a material which is explosive. Thevolume of potentially explosive LAG material stored in small containersmay be sufficient to damage an aircraft or pose a serious safety risk topassengers nearby in an aircraft or in an airport. Proper identificationof LAG materials and their properties during screening operations istherefore important.

In some systems, an object is scanned and an image of the scanned objectis generated for review by human operator such as security personnel atan airport. In other systems, software may be used for the purpose ofprocessing a generated or refined image to identify potentiallythreatening, smuggled or illicit objects or materials. The softwaredetermines whether the pixels of the image represent an object ormaterial of interest and the image may then be forwarded to a humanoperator for second-level screening. In such cases, there is introduceda “human intervention” step and therefore a step whereby human error maybe introduced. For example, a human operator reviewing the image mayfail to identify potentially threatening materials or objects containedin the image. There is also introduced a problem of limited throughputat security stations due to the time required for security personnel toreview the image flagged by the software, as well as the decision-makingprocess for possible rerouting of personnel, baggage and/or passengers.Such human intervention may cause undue delay at the security screeningcheckpoint or may come at prohibitive cost. Moreover, while securitypersonnel review the information provided in the refined image, theirattention is diverted away from their surroundings and therefore awayfrom potentially threatening situations.

Some systems have been put in place to manage passenger throughput atairport security screening checkpoints. However, the reliance on refinedimage data and processing by human operators does not efficientlyaddress the complications associated with steady throughput at securityscreening checkpoints.

In view of the above, advantage would be found with an apparatus andmethod which facilitates automatic analysis of x-ray screeninginformation to limit or eliminate potential for human error and toprocess this information in real time or near real time and preferablyautomatically so as to maintain efficient throughput at locations wherescanning may be performed.

SUMMARY

The present invention relates to x-ray scanning of objects. Moreparticularly, the present invention relates to x-ray scanning of objectsfor determining the properties of the materials of which the objects arecomposed.

In one aspect, there is provided a method for assigning an attribute tox-ray attenuation including the steps of acquiring first and secondreference material equivalent path length information associated with afirst range of dual-energy x-ray attenuation information, acquiringsecond and third reference material equivalent path length informationassociated with a second range of dual-energy x-ray attenuationinformation, and, joining the first the first dual-energy x-rayattenuation information range with the second dual-energy x-rayattenuation information range using coefficients representingdual-energy x-ray attenuation information of the second referencematerial to define a third dual-energy x-ray attenuation informationrange upon which may be imposed dual-energy x-ray attenuation valueswithin the third dual-energy x-ray attenuation information range todetermine corresponding first reference material equivalent path lengthsand third reference material equivalent path lengths.

In one aspect, the step of acquiring first and second reference materialequivalent path length information associated with a first range ofdual-energy x-ray attenuation information further includes the steps ofretrieving from lookup tables saved first and second reference materialequivalent path lengths associated with the dual-energy x-rayattenuation information corresponding with the first dual-energyattenuation information range.

In another aspect, the step of acquiring first and second referencematerial equivalent path length information associated with a firstrange of dual-energy x-ray attenuation information further includes thesteps of scanning in an x-ray scanning device first and second referencematerials each having known atomic composition, known dimensions andknown orientation in the x-ray scanning device. The x-ray scanningdevice emits x-rays which pass through the first reference material withfirst reference material path lengths and through the second referencematerial with second reference material path lengths. The x-rays aredetected by an array of detectors to provide first dual-energy x-rayattenuation information for each of the first and second referencematerials. The method further includes the steps of associating thefirst dual-energy x-ray attenuation information with each of the firstreference material path lengths and the second reference material pathlengths, and, expressing collectively each of the first referencematerial path lengths and the second reference material path lengths asa function of the associated first dual-energy x-ray attenuationinformation to define first dual-energy attenuation surfaces.

In one aspect, the step of expressing collectively each of the firstreference material path lengths and the second reference material pathlengths further includes the step of determining numerically pointwiseinverted first dual-energy attenuation surfaces using an optimizationalgorithm inverting the first dual-energy attenuation surfaces.

In another aspect, the step of expressing collectively each of the firstreference material path lengths and the second reference material pathlengths further includes the step of selecting a model for expressingcollectively each of the first reference material path lengths and thesecond reference material path lengths as a function of the associatedfirst dual-energy x-ray attenuation information to define thedual-energy attenuation surfaces.

The step of selecting the model may further include the steps ofselecting a set of coefficients to be applied to the model for fittingthe first dual-energy x-ray attenuation information with the model, and,fitting the first dual-energy x-ray attenuation information with themodel optimizing the coefficients.

The step of selecting the model may further include the steps ofselecting the set of fitting constraints to be applied to the model forselecting the coefficients, and, selecting the set of coefficients byapplying the set of fitting constraints to the model.

The dual-energy x-ray attenuation information may include high-energyx-ray attenuation information and low-energy x-ray attenuationinformation and the step of associating each of the first low-energyx-ray attenuation information and the first high-energy x-rayattenuation information with each of the first reference material pathlengths and the second reference material path lengths may furtherinclude the steps of defining a first space wherein the first low-energyx-ray attenuation information of the first reference material and thesecond reference material defines a first plane and first referencematerial path lengths and second reference material path lengths eachdefine a first height over the first plane, defining a second spacewherein the first high-energy x-ray attenuation information of the firstreference material and the second reference material defines a secondplane and first reference material path lengths and second referencematerial path lengths each define a second height over second the plane,and, representing collectively the first reference material path lengthsand the second reference material path lengths using the model to definethe first high-energy direct attenuation surface and first low energydirect attenuation surface.

In another aspect, the model is a second model, the first dual-energyattenuation surfaces are first dual-energy inverse attenuation surfaces,respectively, and prior to the associating step, the method furtherincludes the steps of associating each of the first dual-energy x-rayattenuation information with corresponding ones of each of the firstmaterial path lengths and the second material path lengths, and,selecting a first model for expressing collectively the firstdual-energy x-ray attenuation information as a function of the firstreference material path lengths and the second reference material pathlengths to define first direct attenuation surfaces.

The step of selecting the first model may further include the steps ofselecting a first set of coefficients to be applied to the first modelfor fitting the first dual-energy x-ray attenuation information with thefirst model, and, fitting the first dual-energy x-ray attenuationinformation with the first model optimizing the first coefficients. Thestep of selecting the second model further includes the steps ofselecting a second set of coefficients to be applied to the second modelfor fitting the first dual-energy x-ray attenuation information with thesecond model, and, fitting the first dual-energy x-ray attenuationinformation with the second model optimizing the second set ofcoefficients.

The step of selecting the first model may further include the steps ofselecting a first set of fitting constraints to be applied to the firstmodel for selecting the first set of coefficients, and, selecting theset of first coefficients by applying the first set of fittingconstraints to the first model. The step of selecting second model mayfurther include the steps of selecting a second set of fittingconstraints to be applied to the second model for selecting the secondset of coefficients, and, selecting the second set of coefficients byapplying the second set of fitting constraints to the second model.

The dual-energy x-ray attenuation information may include high-energyx-ray attenuation information and low-energy x-ray attenuationinformation and the associating step may further include the steps ofdefining a space wherein the first reference material path lengths andthe second reference material path lengths define a first plane and thefirst high-energy x-ray attenuation information and the first low-energyx-ray attenuation information each define a respective first and secondheight over the first plane and representing collectively the firsthigh-energy x-ray attenuation information and the first low-energy x-rayattenuation information using the first model to define the firsthigh-energy direct attenuation surface and first low energy directattenuation surface, defining an inverse space wherein the firstlow-energy x-ray attenuation information and the first high-energy x-rayattenuation information define a second plane and first referencematerial path lengths and second reference material path lengths eachdefine a respective third and fourth height over the second plane, and,representing collectively the first reference material path lengths andthe second reference material path lengths using the second model todefine first high-energy and first low-energy inverse attenuationsurfaces.

In one aspect, the step of acquiring second and third reference materialequivalent path length information associated with a second range ofdual-energy x-ray attenuation information further includes the step ofretrieving from lookup tables saved second and third reference materialequivalent path lengths associated with the dual-energy x-rayattenuation information corresponding with the second dual-energyattenuation information range.

In one aspect, the step of expressing collectively each of the secondreference material path lengths and the third reference material pathlengths further includes the step of determining numerically pointwiseinverted second dual-energy attenuation surfaces using an optimizationalgorithm inverting the second dual-energy attenuation surfaces.

In another aspect, the step of acquiring second and third referencematerial equivalent path length information associated with a firstrange of dual-energy x-ray attenuation information further includes thesteps of scanning in the x-ray scanning device the second referencematerial and a reference third material having known atomic composition,known dimensions and known orientation in the x-ray scanning device toprovide second low-energy x-ray attenuation information and high-energyx-ray attenuation information for each of the second and third referencematerials, associating each of the second low-energy x-ray attenuationinformation and the second high-energy x-ray attenuation informationwith each of the second reference material path lengths and thirdreference material path lengths, and, expressing collectively each ofthe second reference material path lengths and the third referencematerial path lengths as a function of the associated low-energy x-rayattenuation information and high-energy x-ray attenuation information todefine second high-energy attenuation surfaces and second low-energyattenuation surfaces.

In another aspect, the step of expressing collectively each of thesecond reference material path lengths and the third reference materialpath lengths further includes the step of selecting a model forexpressing collectively each of the second reference material pathlengths and the third reference material path lengths as a function ofthe associated second dual-energy x-ray attenuation information todefine the second dual-energy attenuation surfaces.

The step of selecting the model may further include the steps ofselecting a set of coefficients to be applied to the model for fittingthe second dual-energy x-ray attenuation information with the model,and, fitting the second dual-energy x-ray attenuation information withthe model optimizing the coefficients.

The step of selecting the model may further include the steps ofselecting the set of fitting constraints to be applied to the model forselecting the coefficients, and, selecting the set of coefficients byapplying the set of fitting constraints to the model.

The dual-energy x-ray attenuation information may include high-energyx-ray attenuation information and low-energy x-ray attenuationinformation and the step of associating each of the second low-energyx-ray attenuation information and the second high-energy x-rayattenuation information with each of the second reference material pathlengths and third reference material path lengths may further includethe steps of defining a first space wherein the second low-energy x-rayattenuation information of the second reference material and the thirdreference material defines a first plane and second reference materialpath lengths and third reference material path lengths each define afirst height over the first plane, defining a second space wherein thesecond high-energy x-ray attenuation information of the second referencematerial and the third reference material defines a second plane andsecond reference material path lengths and third reference material pathlengths each define a second height over second the plane, and,representing collectively the second reference material path lengths andthe third reference material path lengths using the model to define thesecond high-energy direct attenuation surface and second low energydirect attenuation surface.

In another aspect, the model is a second model, the second dual-energyattenuation surfaces are second dual-energy inverse attenuationsurfaces, respectively, and prior to the associating step, the methodfurther includes the steps of associating each of the second dual-energyx-ray attenuation information with corresponding ones of each of thesecond material path lengths and the third material path lengths, and,selecting a first model for expressing collectively the seconddual-energy x-ray attenuation information as a function of the secondreference material path lengths and the third reference material pathlengths to define second direct attenuation surfaces.

The step of selecting the first model may further include the steps ofselecting a first set of coefficients to be applied to the first modelfor fitting the second dual-energy x-ray attenuation information withthe first model, and, fitting the second dual-energy x-ray attenuationinformation with the first model optimizing the first coefficients. Thestep of selecting the second model may further include the steps ofselecting a second set of coefficients to be applied to the second modelfor fitting the second dual-energy x-ray attenuation information withthe second model, and, fitting the second dual-energy x-ray attenuationinformation with the second model optimizing the second set ofcoefficients.

The step of selecting the first model may further include the steps ofselecting a first set of fitting constraints to be applied to the firstmodel for selecting the first set of coefficients, and, selecting theset of first coefficients by applying the first set of fittingconstraints to the first model. The step of selecting second the modelmay further include the steps of selecting a second set of fittingconstraints to be applied to the second model for selecting the secondset of coefficients, and, selecting the second set of coefficients byapplying the second set of fitting constraints to the second model.

The associating step may further include defining a space wherein thesecond reference material path lengths and the third reference materialpath lengths define a first plane and the second high-energy x-rayattenuation information and the second low-energy x-ray attenuationinformation each define a respective first and second height over thefirst plane and representing collectively the second high-energy x-rayattenuation information and the second low-energy x-ray attenuationinformation using the first model to define the second high-energydirect attenuation surface and second low energy direct attenuationsurface, defining an inverse space wherein the second low-energy x-rayattenuation information and the second high-energy x-ray attenuationinformation define a second plane and second reference material pathlengths and third reference material path lengths each define arespective third and fourth height over the second plane, and,representing collectively the second reference material path lengths andthe third reference material path lengths using the second model todefine second high-energy and second low-energy inverse attenuationsurfaces.

The step of joining the first the first dual-energy x-ray attenuationinformation range with the second dual-energy x-ray attenuationinformation range may further include the steps of selecting a firstmodel for expressing collectively each of the first reference materialpath lengths and the second reference material path lengths as afunction of the associated first dual-energy x-ray attenuationinformation range, selecting a first set of coefficients to be appliedto the first model for fitting the first dual-energy x-ray attenuationinformation range with the first model, selecting a second model forexpressing collectively each of the second reference material pathlengths and the third reference material path lengths as a function ofthe associated second dual-energy x-ray attenuation information range,selecting a second set of coefficients to be applied to the second modelfor fitting the second dual-energy x-ray attenuation information rangewith the second model, weighting to a zero value the coefficients forfitting the dual-energy x-ray attenuation information of the firstreference material to the first model to obtain a subset of coefficientsfor fitting respective dual-energy x-ray attenuation information of onlythe second reference material to either of the first model and thesecond model, and, fitting the first set of coefficients with the secondset of coefficients using the subset of coefficients to join the firstmodel and the second model to provide the third dual-energy x-rayattenuation information range.

In another aspect, there is provided a method for assigning an attributeto x-ray attenuation including the steps of acquiring first and secondreference material equivalent path length information associated with afirst range of dual-energy x-ray attenuation information by a firstmodel for expressing collectively each of the first reference materialpath lengths and the second reference material path lengths as afunction of the associated first range of dual-energy x-ray attenuationinformation, the first range of dual-energy attenuation informationbeing fitted with the first model by a first set of coefficients,acquiring third reference material equivalent path length informationassociated with a second range of dual-energy x-ray attenuationinformation by a second model for expressing collectively each of thethird reference material equivalent path lengths as a function of theassociated second range of dual-energy attenuation information, thesecond range of dual-energy being fitted with the second model by asecond set of coefficients, the third reference material having aneffective atomic number greater than that of the second referencematerial, combining the first set of coefficients and the second set ofcoefficients to provide a third set of coefficients for fitting thefirst and second range of dual-energy x-ray attenuation information witha third model for expressing collectively the first and third referencematerial path lengths as a function of the fitted first and second rangeof dual-energy x-ray attenuation information, and, for all points in thethird model determine a volume fraction of one of the first and thethird reference material which represents the second reference materialpath lengths to identify where in the third model path lengthsrepresenting the second reference material are represented.

In one aspect, the step of acquiring first and second reference materialequivalent path length information associated with a first range ofdual-energy x-ray attenuation information further includes the steps ofretrieving from lookup tables saved first and second reference materialequivalent path lengths associated with the dual-energy x-rayattenuation information corresponding with the first dual-energyattenuation information range.

In another aspect, the step of acquiring first and second referencematerial equivalent path length information associated with a firstrange of dual-energy x-ray attenuation information further includes thesteps of scanning in an x-ray scanning device first and second referencematerials each having known atomic composition, known dimensions andknown orientation in the x-ray scanning device. The x-ray scanningdevice emits x-rays which pass through the first reference material withfirst reference material path lengths and through the second referencematerial with second reference material path lengths. The x-rays aredetected by an array of detectors to provide first dual-energy x-rayattenuation information for each of the first and second referencematerials. The method further includes the steps of associating thefirst dual-energy x-ray attenuation information with each of the firstreference material path lengths and the second reference material pathlengths, and, expressing collectively each of the first referencematerial path lengths and the second reference material path lengths asa function of the associated first dual-energy x-ray attenuationinformation to define first dual-energy attenuation surfaces.

In one aspect, the step of expressing collectively each of the firstreference material path lengths and the second reference material pathlengths further includes the step of determining numerically pointwiseinverted first dual-energy attenuation surfaces using an optimizationalgorithm inverting the first dual-energy attenuation surfaces.

In another aspect, the step of expressing collectively each of the firstreference material path lengths and the second reference material pathlengths further includes the step of selecting a model for expressingcollectively each of the first reference material path lengths and thesecond reference material path lengths as a function of the associatedfirst dual-energy x-ray attenuation information to define thedual-energy attenuation surfaces.

The step of selecting the model may further include the steps ofselecting a set of coefficients to be applied to the model for fittingthe first dual-energy x-ray attenuation information with the model, and,fitting the first dual-energy x-ray attenuation information with themodel optimizing the coefficients.

The step of selecting the model may further include the steps ofselecting the set of fitting constraints to be applied to the model forselecting the coefficients, and, selecting the set of coefficients byapplying the set of fitting constraints to the model.

The dual-energy x-ray attenuation information may include high-energyx-ray attenuation information and low-energy x-ray attenuationinformation and the step of associating each of the first low-energyx-ray attenuation information and the first high-energy x-rayattenuation information with each of the first reference material pathlengths and the second reference material path lengths may furtherinclude the steps of defining a first space wherein the first low-energyx-ray attenuation information of the first reference material and thesecond reference material defines a first plane and first referencematerial path lengths and second reference material path lengths eachdefine a first height over the first plane, defining a second spacewherein the first high-energy x-ray attenuation information of the firstreference material and the second reference material defines a secondplane and first reference material path lengths and second referencematerial path lengths each define a second height over second the plane,and, representing collectively the first reference material path lengthsand the second reference material path lengths using the model to definethe first high-energy direct attenuation surface and first low energydirect attenuation surface.

In another aspect, the model is a second model, the first dual-energyattenuation surfaces are first dual-energy inverse attenuation surfaces,respectively, and prior to the associating step, the method furtherincludes the steps of associating each of the first dual-energy x-rayattenuation information with corresponding ones of each of the firstmaterial path lengths and the second material path lengths, and,selecting a first model for expressing collectively the firstdual-energy x-ray attenuation information as a function of the firstreference material path lengths and the second reference material pathlengths to define first direct attenuation surfaces.

The step of selecting the first model may further include the steps ofselecting a first set of coefficients to be applied to the first modelfor fitting the first dual-energy x-ray attenuation information with thefirst model, and, fitting the first dual-energy x-ray attenuationinformation with the first model optimizing the first coefficients. Thestep of selecting the second model further includes the steps ofselecting a second set of coefficients to be applied to the second modelfor fitting the first dual-energy x-ray attenuation information with thesecond model, and, fitting the first dual-energy x-ray attenuationinformation with the second model optimizing the second set ofcoefficients.

The step of selecting the first model may further include the steps ofselecting a first set of fitting constraints to be applied to the firstmodel for selecting the first set of coefficients, and, selecting theset of first coefficients by applying the first set of fittingconstraints to the first model. The step of selecting second model mayfurther include the steps of selecting a second set of fittingconstraints to be applied to the second model for selecting the secondset of coefficients, and, selecting the second set of coefficients byapplying the second set of fitting constraints to the second model.

The dual-energy x-ray attenuation information may include high-energyx-ray attenuation information and low-energy x-ray attenuationinformation and the associating step may further include the steps ofdefining a space wherein the first reference material path lengths andthe second reference material path lengths define a first plane and thefirst high-energy x-ray attenuation information and the first low-energyx-ray attenuation information each define a respective first and secondheight over the first plane and representing collectively the firsthigh-energy x-ray attenuation information and the first low-energy x-rayattenuation information using the first model to define the firsthigh-energy direct attenuation surface and first low energy directattenuation surface, defining an inverse space wherein the firstlow-energy x-ray attenuation information and the first high-energy x-rayattenuation information define a second plane and first referencematerial path lengths and second reference material path lengths eachdefine a respective third and fourth height over the second plane, and,representing collectively the first reference material path lengths andthe second reference material path lengths using the second model todefine first high-energy and first low-energy inverse attenuationsurfaces.

The step of acquiring third reference material equivalent path lengthinformation associated with a second range of dual-energy x-rayattenuation information may further include the steps of retrieving fromlookup tables saved third reference material equivalent path lengthsassociated with the dual-energy x-ray attenuation informationcorresponding with the second dual-energy attenuation information range.

The step of acquiring third reference material equivalent path lengthinformation associated with a second range of dual-energy x-rayattenuation information may further include the steps of, scanning inthe x-ray scanning device the third reference material having knownatomic composition, known dimensions and known orientation in the x-rayscanning device to provide second dual-energy x-ray attenuationinformation for the third reference material, associating each of thesecond dual-energy x-ray attenuation information with the thirdreference material path lengths, and, expressing collectively the thirdreference material path lengths as a function of the associateddual-energy x-ray attenuation information to define second dual-energyattenuation surfaces.

The step of fitting the second range of dual-energy attenuationinformation with the second model by a second set of coefficients mayfurther include the step of fitting the second range of dual-energyx-ray attenuation information with the second model to optimize thesecond set of coefficients.

The step of fitting the second range of dual-energy attenuationinformation with the second model by a second set of coefficients mayfurther includes the steps of selecting a set of fitting constraints tobe applied to the second model for selecting the second set ofcoefficients, and, selecting the second set of coefficients by applyingthe set of fitting constraints to the second model.

The dual-energy x-ray attenuation information may includes high-energyx-ray attenuation information and low-energy x-ray attenuationinformation and the step of associating the second range of dual-energyx-ray attenuation information with the third reference material pathlengths may further include the steps of defining a first space whereinthe second low-energy x-ray attenuation information of the thirdreference material defines a first plane and the third referencematerial path lengths define a first height over the first plane,defining a second space wherein the second high-energy x-ray attenuationinformation of the third reference material defines a second plane andthe third reference material path lengths define a second height oversecond the plane, and, representing collectively the third referencematerial path lengths using the second model to define seconddual-energy direct attenuation surfaces.

The dual-energy x-ray attenuation information may include high-energyx-ray attenuation information and low-energy x-ray attenuationinformation and may further include the steps of defining a spacewherein the first reference material path lengths and the thirdreference material path lengths define a first plane and the first andsecond high-energy x-ray attenuation information and the first andsecond low-energy x-ray attenuation information each define a respectivefirst and second height over the first plane and the third modelexpresses collectively the first and third reference material pathlengths as a function of the first and second low-energy x-rayattenuation and the first and second high-energy x-ray attenuation todefine a third dual-energy direct attenuation surface, defining aninverse space wherein the first and second low-energy x-ray attenuationinformation and the first and second high-energy x-ray attenuationinformation define a second plane and first reference material pathlengths and third reference material path lengths each define arespective third and fourth height over the second plane, and,representing collectively the first reference material path lengths andthe third reference material path lengths using the third model todefine dual-energy inverse attenuation surfaces.

In another aspect, there is provided a method for assigning an attributeto x-ray attenuation including the steps of acquiring first and secondreference material equivalent path length information associated with afirst range of dual-energy x-ray attenuation information by a model forexpressing collectively each of the first reference material pathlengths and the second reference material path lengths as a function ofthe associated first range of dual-energy x-ray attenuation information,selecting an extrapolation range of dual-energy x-ray attenuationinformation over which first and second reference material path lengthsare to be associated with dual-energy x-ray attenuation information of afirst imposed material having a predetermined minimum effective atomicnumber less than an effective atomic number of the first referencematerial and a second imposed material having a predetermined maximumeffective atomic number greater than an effective atomic number of thesecond reference material, wherein the first range is within theextrapolation range, selecting a set of fitting constraints forassociating each of the first reference material path lengths and thesecond reference material path lengths over the extrapolation range ofdual-energy attenuation information to define extrapolated first andsecond reference material equivalent path lengths over the extrapolationrange, and, applying the set of fitting constraints to the model.

In one aspect, the step of acquiring first and second reference materialequivalent path length information associated with a first range ofdual-energy x-ray attenuation information may further include the stepsof retrieving from lookup tables saved first and second referencematerial equivalent path lengths associated with the dual-energy x-rayattenuation information corresponding with the first range ofdual-energy x-ray attenuation information.

The step of acquiring first and second reference material equivalentpath length information associated with a first range of dual-energyx-ray attenuation information may further include the steps of scanningin an x-ray scanning device first and second reference materials eachhaving known atomic composition, known dimensions and known orientationin the x-ray scanning device, the x-ray scanning device emitting x-rayswhich pass through the first reference material with first referencematerial path lengths and through the second reference material withsecond reference material path lengths, the x-rays being detected by anarray of detectors to provide first dual-energy x-ray attenuationinformation for each of the first and second reference materials,associating the first dual-energy x-ray attenuation information witheach of the first reference material path lengths and the secondreference material path lengths, and, using the model to expresscollectively each of the first reference material path lengths and thesecond reference material path lengths as a function of the associatedfirst dual-energy x-ray attenuation information to define firstdual-energy attenuation surfaces.

The step of applying the set of fitting constraints to the model mayfurther include the step of selecting a set of coefficients to beapplied to the model for fitting the dual-energy x-ray attenuationinformation of the first range with the model, and, fitting, using theset of fitting constraints, the dual-energy x-ray attenuationinformation of the extrapolation range with the model.

The dual-energy x-ray attenuation information may include high-energyx-ray attenuation information and low-energy x-ray attenuationinformation and associating each of the first and second referencematerial path lengths with the first range of dual-energy x-rayattenuation information may further include the steps of defining afirst space wherein the low-energy x-ray attenuation information of thefirst reference material and the second reference material defines afirst plane and first reference material path lengths and secondreference material path lengths each define a first height over thefirst plane, defining a second space wherein the high-energy x-rayattenuation information of the first reference material and the secondreference material defines a second plane and first reference materialpath lengths and second reference material path lengths each define asecond height over second the plane, and, representing collectively thefirst reference material path lengths and the second reference materialpath lengths using the first model to define the dual-energy directattenuation surfaces.

The dual-energy x-ray attenuation information may include high-energyx-ray attenuation information and low-energy x-ray attenuationinformation and the step of selecting a second model may further includethe steps of defining a first space wherein the low-energy x-rayattenuation information of the first imposed material and the secondimposed material defines a first plane and first imposed material pathlengths and second imposed material path lengths each define a firstheight over the first plane, defining a second space wherein thehigh-energy x-ray attenuation information of the first imposed materialand the second imposed material defines a second plane and first imposedmaterial path lengths and second imposed material path lengths eachdefine a second height over second the plane, and, representingcollectively the first imposed material path lengths and the secondimposed material path lengths using the second model to define theextrapolated dual-energy direct attenuation surfaces.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of an exemplary x-ray scanning device whichmay be used in association with the present invention;

FIG. 2 is an illustration of a system which may be used in associationwith the present invention;

FIG. 3 is a flow chart representing the calibration method of thepresent invention;

FIG. 4 is a flow chart representing the method for modeling ofdual-material equivalent path lengths as a function of the dual-energysignal as shown in FIG. 3;

FIG. 5 is an example plane wherein the dual-energy x-ray attenuationsmeasured by a detector are represented on the z axis, the first materialpath length values t₁ are represented on the x axis and the secondmaterial path length values t₂ are represented on the y axis;

FIG. 6 is an example three-dimensional space wherein the referencematerial path length values for each pixel representing the referencematerials define a plane and wherein a z-axis also represents thecorresponding measured HE and LE x-ray attenuation as a height off ofthe plane;

FIG. 7 shows an example step wedge as may be used in association withthe present invention;

FIG. 8 shows a fitted direct attenuation surface with data points usedfor the fitting for the low-energy domain;

FIG. 9 shows a fitted direct attenuation surface with data points usedfor the fitting for the high-energy domain;

FIG. 10A shows an inverted attenuation surface for the first referencematerial path lengths t₁;

FIG. 10B shows an inverted attenuation surface for the second referencematerial path lengths t₂;

FIG. 11 is a flow chart representing the method for assigning effectiveatomic number values to the first and second reference materialattenuation as shown in FIG. 3;

FIG. 12 is a flow chart representing the method for assigning massthickness to the first and second reference material attenuation asshown in FIG. 3;

FIG. 13 is a flow chart representing the method for assigning aneffective atomic number value to an unknown object;

FIG. 14 is a flow chart representing one aspect of a method for removinga predetermined background object from an image;

FIG. 15 is an example representation of the object and background pathlengths showing an overlap region;

FIG. 16 is a flow chart representing another aspect of method forremoving a background object from an image;

FIGS. 17A & B are a flow chart representing another aspect of method forremoving a background object from an image;

FIG. 18 is a flow chart representing one aspect of a method forextending a range of calibration information;

FIG. 19 is a representation of the method shown in FIG. 18;

FIG. 20 is another aspect of the method for extending a range ofcalibration information;

FIG. 21 is another aspect of the method for extending a range ofcalibration information;

FIG. 22 is a representation of the method shown in FIG. 21;

FIGS. 23A & B are a flow chart representing one aspect of a method forreconstructing an unknown object contained within a container;

FIG. 24 is a flow chart representing one aspect of a method for removinga background object as part of the method for reconstructing an unknownobject;

FIG. 25 is a flow chart representing another aspect of a method forremoving a background object as part of the method for reconstructing anunknown object;

FIG. 26 is a flow chart representing one aspect of a method forreconstructing an unknown object; and,

FIG. 27 is a flow chart representing one aspect of a method fordetermining a safe of threat condition for an unknown object.

DESCRIPTION

The present invention relates to x-ray scanning of objects. Moreparticularly, the present invention relates to x-ray scanning of objectsfor determining the properties of the materials of which the objects arecomposed.

The present invention provides methods and apparatuses which aresuitable for detection of potentially harmful objects scanned in anx-ray scanning device which provides for automatic and real time or nearreal time analysis of the information provided.

According to the aspect shown in FIG. 1, there is provided an x-rayscanning device 100. The x-ray scanning device 100 includes a housing102 having openings 104 at either end thereof. The openings 104 provideaccess to a scanning chamber 106 passing through the housing 102. Thesystem 100 may further include a displacement assembly 108, such as aconveyor, which extends through the scanning chamber 106 and which maybe used to displace at least one object of interest to be scanned usingthe x-ray scanning device 100.

The term “object” as used herein refers to any object of interest, knownor unknown, for scanning purposes and is not necessarily limited to aspecific shape, size, composition or configuration. The object ofinterest may be a singular object composed of one or more materials,such as for example, a liquid material contained within a container, ormay include a plurality of objects targeted for scanning, such as forexample, the contents of a bag of luggage.

The x-ray scanning device 100 further includes a source assembly 110.The source assembly 110 includes a source (not shown) for emittingelectromagnetic radiation such as x-rays, a source assembly housing 112at least partially enclosing the source, a pedestal 114 to which thesource assembly housing 112 is mounted and a collimator 116 mounted tothe source assembly housing 112 for directing x-rays emitted from thesource. Collimator 116 may be of any suitable shape but is preferably afan-shaped collimator for directing the x-rays in a fan-shaped beam.Moreover, the pedestal 114 is not required and may not necessarily bepresent in some x-ray scanning devices suitable for the purposes of thepresent invention.

The x-ray scanning device 100 may further include a group of detectorsincluding at least one detector card 120 and preferably a plurality ofdetector cards 120 each mounted to the bracket 122. It should beunderstood to a person skilled in the art that the detector may be in aform other than a detector card that would be suitable for the purposesof the present invention. In one aspect, the bracket is an L-shapedbracket which is positioned outside the scanning chamber 106 such thatthe plurality of detector cards 120 mounted thereto extend into thescanning chamber 106. In some aspects, the bracket 122 may be locatedwithin the scanning chamber. In the aspect shown in FIG. 1 there isshown mounted within the scanning chamber a single bracket 122. Itshould be understood that in other aspects, the scanning chamber mayinclude more than one bracket positioned within the scanning chamber andthat the brackets do not have to have the same orientation or angularposition. It should be further understood that the bracket 122 does nothave to be L-shaped. Rather, the bracket 122 may be linear or arc shapedor any other suitable shape.

In some embodiments, each detector card 120 includes at least oneindividual detector. As shown in FIG. 2, detector cards 120 and thex-ray scanning device 100 may be linked to a central processing unit(CPU) 200 or other processing device so that x-ray signals detected bythe detector cards 120 may be analyzed, processed, and used to outputinformation, is further disclosed herein. The processor 200 and itsassociated architecture may be used to implement any of the processes ormethods described herein as well as one or more of their associatedsteps either automatically or in real-time or both.

According to the aspect shown in FIG. 2, each detector card 120 maycomprise a first scintillator material 202, a filter 204 and a secondscintillator material 206. All of these may be sandwiched together orotherwise suitably arranged as shown in FIG. 2. In a scanning operation,broad x-ray spectral intensity is emitted by the source and is directedby the collimator 116 toward the plurality of detector cards 120 withinthe scanning chamber 106. In the case of each detector card 120, aplurality of the emitted x-rays encounter the first scintillatormaterial 202 which may be configured to detect preferentially the lowerportion of the emitted x-ray spectral intensity. The spectral intensityof x-rays may then be stopped by the filter 204 and remaining x-rays'spectral intensity reach the second scintillator material 206. Due tothe transmission through the first scintillator material 202 and thefilter 204, the x-rays spectral intensity reaching the secondscintillator material 206 contains a higher portion of high-energyx-rays than the x-rays spectral intensity reaching the firstscintillator material 202.

In the context of the present description, the term “processor” refersto at least one computerized component for executing computer-executableinstructions. This may include, for example, a central processing unit(CPU), a microprocessor, a controller, and/or the like. A plurality ofsuch processors may be provided, according to different aspects of thepresent invention, as can be understood by a person skilled in the art.The processor may be provided within one or more general-purposecomputers, for/or any other suitable computing device.

The term “storage” may refer to any computer data storage device orassembly of such devices including, for example, a temporary storageunit such as random-access memory (RAM) or dynamic RAM, permanentstorage medium such as a hard disk, and optical storage device, such asa CD or DVD (rewritable or write once/read only), a flash memory, adatabase, and/or the like. A plurality of such storage devices may beprovided, as can be understood by a person skilled in the art.

With further reference to FIG. 2, in one aspect, each of thesescintillator materials 202, 206 converts the absorbed x-ray energy toinfrared, visible and ultraviolet light. Each of these scintillatormaterials 202, 206 is coupled with a photodiode 208 which captures thelight from the respective scintillator 202, 206 and generates acorresponding analog electric signal. The analog electric signal isfurther digitized by a converter 210. The digitized signal value isassociated with a pixel of an image for providing a visualrepresentation of an object being scanned.

In the conversion of the infrared, visible and ultraviolet light into ananalog electric signal by the photodiodes 208, some uncertainties may beintroduced, in that a given x-ray spectral intensity may result in adifferent infrared, visible and ultraviolet light source which may alsoresult in different analog electric signals due to the fact that everydetector in every detector card may react slightly differently to thepresence of electromagnetic radiation. Slight variations in the x-rayand/or light sources may be taken into account in all methods describedherein. In order to correct these variations and for the final image toappear more homogeneously, each pixel of the image may be normalized bycorrecting an offset and gain in the light conversion. The normalizationprocedure may be executed for example using a normalization module 212as shown in FIG. 2 in order to compensate for slight variations inoffset and gain for each detector, as well as for estimating theexpected uncertainties in low-energy and high-energy signals and/orattenuations for each detector.

The apparatus may further include a dual-material decomposition module214 for decomposing low-energy and high-energy signals and/orattenuations of known or unknown scanned materials into correspondingreference material attribute information, a mass thickness determinationmodule 216 for determining the mass thickness of one or more objects ofinterest, an effective atomic number module 218 for determining theeffective atomic number of one or more objects or materials of interest,a background removal module 220 for distinguishing one object ormaterial from another in a dual-energy image and removing high andlow-energy x-ray signal information associated with specific objectswhich may not necessarily be of interest, a reconstruction module 222for reconstructing an object of interest once high and low-energy x-raysignal information associated with the specific not-of-interest objectshave been removed and a threat determination module 224 for determiningwhether one or more objects or materials of interest pose a threat andcorrespondingly raising an alarm condition based on the determination.Information acquired by any of the aforementioned modules may be savedto a suitable storage medium such as a database 226. Moreover, imagesmay be output to a display 228.

Calibration Method

This calibration method described herein is directed to acquiringreference data and deriving values representative of the real-world usedfor the purpose of computing images representing physical properties ofscanned objects from dual-energy transmission images.

In one aspect, the source emits x-rays across an energy spectrum, from 0keV to the energy corresponding to the peak voltage of the source. Thepeak voltage may be, for example, 160 kVp. The spectrum S(E) is afunction taking, in general, non-zero positive values all over theenergy range 0 keV to 160 keV. This spectrum will be detected by twoarrays of detectors stacked on top of each other. The array closest tothe source is the low-energy (LE) detector and preferentially absorbsx-rays with low-energies among all the energies available in thespectrum. The x-rays that are not absorbed by the LE detectors, passthrough the LE detectors and those which are not filtered out by thefilters reach the high-energy (HE) detectors, which absorbs x-rays withhigher energies due the hardening of the spectral intensity of thex-rays. The materials composing the detectors may also induce adifference in the energies they absorb. The low-energy x-ray signals andthe high-energy x-ray signals may be collectively referred to as“dual-energy signals”. Likewise, properties of or derived independentlyfrom both high-energy x-ray signals and low-energy x-ray signals, suchas attenuation or images, for example, may likewise be referred to as“dual-energy”. Moreover, since a detector includes both high-energy andlow-energy detectors, the detectors themselves may sometimes be referredto as “dual-energy detectors”. A person skilled in the art willappreciate that dual-energy signals can also be generated by othermeans, such as switching the peak voltage of the source or by using twosources, but different fixed peak voltages. In these embodiments, onlyone scintillator material for each of the detector arrays associatedwith each of the source would be required to acquire the dual-energysignals.

The method described herein includes decomposing dual-energy x-rayattenuation images into reference material path length images.Preferably, two reference materials are used to provide the basis forthe reference material path length images. Accordingly, the set ofimages provided by the two reference materials may be collectivelyreferred to as the “dual-material” or the “reference material” pathlength images. The reference material path length images allow thefurther computation of both the mass thickness and effective atomicnumber of an object of interest. The mass density of the object ofinterest may then be deduced from the mass thickness and the pathlengths of the object of interest. The dual-material path lengthdecomposition approach includes the acquisition of reference data fromreference objects, such as step wedges, composed of two differentmaterials scanned in several different configurations and orientationswithin the scanning device, as is discussed in further detailhereinafter. FIG. 7 shows an example step wedge composed of 2 plates ofABS stacked on top of 8 plates of Aluminum. The materials composing thestep wedges may include any homogeneous material such as, for example,plexiglass, aluminum and/or steel. The step wedge materials arepreferably in the form of plates which may have different lengths andthicknesses but each plate is preferably of uniform thickness. Anexample step wedge may include 10 steps built by stacking plates made oftwo basis materials on top of each other or otherwise suitably arranged.The steps in the step wedge may be varied in their composition bychanging the stacking order of the plates of material and the number ofplates of each basis material used in the assembly. For the purposes ofproviding a basis for decomposition of x-ray attenuation images intoreference material path length images, the dual-material step wedges areof known configuration and thickness and are composed of known materialshaving known atomic composition and mass density. The thickness of eachstep in the step wedge may be measured directly on the step wedge usinga measurement tool such as a caliper. Also known are the relativepositions of the detectors with respect to their associated source. Thisinformation is available from the mechanical design of the x-ray scanneror may be determined by other suitable means.

Assignment of Path Lengths to Reference Materials

In a first aspect as shown in FIG. 3, there is provided a method 300 forassigning an attribute, such as reference material path lengths, tox-ray attenuation information. In a first step 302, dual-referencematerials are scanned, such as a dual-material step wedge havingcomposed of first and second reference materials, preferably in morethan one orientation, such as flat on the conveyor belt or on one of itssides and in more than one position within the x-ray scanner such thatall active detectors detect the profile of the step wedge in at leastone position. Thereby, there is provided dual-material calibration dataas in step 304. During each scan of the dual-material step wedge, x-rayspass through the dual-material step wedge to be detected by detectors.The detected x-rays produce dual-energy x-ray signals, which may includelow-energy x-ray signals and high-energy x-ray signals. These signalsmay be used to generate a high-energy (HE) domain image and a low-energy(LE) domain image. Together, the high-energy domain image and thelow-energy domain image may be referred to as a “dual-energy image” or a“set of dual-energy images”. Each of the high-energy domain image andthe low-energy domain image is composed of a plurality of pixelsdistributed in columns and rows. Each high-energy domain image andlow-energy domain image of the scanned dual-material step wedges may besaved in a suitable storage medium such as an information database.

In each LE domain image and/or HE domain image, there will be determineda region-of-interest (ROI). The ROI represents the pixels of the LE orHE domain image representing the scanned step wedge The ROI may excludeamong other things the transitions between the steps of the step wedgeand other parts of the step wedge used to ensure its mechanicalintegrity such as, for example, bolts, nuts and sustaining rack. In viewof this, it should be understood that the entire image or parts of itmay be considered as a whole in order to determine information morecomplex than that provided by a single pixel.

A path length is the length of the path of an x-ray directed from thesource focal point passing through the material to a given detector.Since the thickness of each material of the dual-material step wedge isknown, the orientation of the dual-material step wedge within the x-rayscanner is known and the position of the source and all active detectorsis known, the path length of the x-rays through material may becalculated for all active detectors. In one aspect, these calculatedvalues may further be placed in a database for storing step wedgematerial path length values for later retrieval.

The reference material path lengths are mathematical variables derivedfrom the low-energy x-ray attenuation and high-energy x-ray attenuationwhich corresponds with the path length of the x-rays through acorresponding location in the reference material. The reference materialpath lengths through a scanned material may be represented usingnotation t_(m), m=1, 2. For scanned reference materials, the first andsecond reference material path lengths are measured and take specificknown values denoted as {circumflex over (t)}_(m), m=1, 2. Therefore,the first reference material path length t₁ may take correspondingmeasured first reference material path length values {circumflex over(t)}₁. The second reference material path length t₂ may takecorresponding measured second reference material path length value{circumflex over (t)}₂. Further use of the expressions “first materialpath lengths” and “second material path lengths” may refer to either themathematical variables t_(m), m=1, 2 derived from the low-energy x-rayattenuation and high-energy x-ray attenuation or the corresponding known(measured) values {circumflex over (t)}_(m), m=1, 2, as a person skilledin the art would recognize.

The dual reference material path length values t₁ and t₂ may then beassociated or modeled in step 306 as a function of the measured high andlow-energy x-ray attenuation values. In general, the high and low-energyattenuation A associated with the high and low-energy normalized signalI is given by

$A = {- {\ln\left( \frac{I}{R} \right)}}$where R is an arbitrary strictly positive constant called thenormalization range and is equal to the normalized signal when no objectis scanned. In view of this, it should be understood to a person skilledin the art that the low-energy or high-energy signal I and low-energy orhigh-energy attenuation A may be used interchangeably by a personskilled in the art, and may be used interchangeably herein, withoutdeparting from the scope of the invention.

Once the dual reference material path length values are modeled as afunction of the dual-energy signal, as in step 306, the values may besaved in corresponding lookup tables for more efficient determination ofthe equivalent path lengths of the first reference material associatedwith a particular x-ray attenuation as in step 308 and for the pathlengths of the second reference material as in step 310. It should beunderstood that “equivalent” does not necessarily mean perfect physicalor geometric equivalence. The term “equivalent” as used herein may referto close approximation or modeling of the actual physical characteristicof a physical material or object, such as, for example, x-ray pathlengths, effective atomic number and mass thickness. As with any modeledphysical characteristic, there may be a slight difference between themeasured physical characteristic and the modeled physicalcharacteristic. The method may then proceed to step 312 wherein the pathlength information may be used as a basis for assigning mass thicknessvalues to the dual-energy x-ray attenuation for each of the referencematerials. Such mass thickness values may likewise be saved in massthickness lookup tables as in step 314 for more efficient determinationof the mass thickness values associated with dual-energy x-rayattenuation associated with each of the first and second referencematerials. Step 312 is discussed in further detail hereinafter. Once thefirst and second reference material path lengths are associated withspecific x-ray energy attenuation information provided by scanning thefirst and second reference materials, the first and second referencematerial path lengths may be used to subsequently determine anappropriate effective atomic number, or Z_(eff), to be assigned to thecorresponding x-ray attenuation information as in step 316. This step isdiscussed in further detail hereinafter. Moreover, it should beunderstood that this step 316 may be performed in advance of, inconjunction with or independently of step 312. The associated effectiveatomic number values may be saved in lookup tables for more efficientreference in future operations as shown in step 318.

The step 306 for modeling of the dual-material equivalent path lengthsas a function of the dual-energy attenuation signal is further definewith reference to FIG. 4 wherein a three-dimensional space may then bedefined for each of the measured high and low-energy x-ray signalswherein material path length values t₁ through the first material andmaterial path length values t₂ through the second material define points(t₁, t₂) forming a plane and each of the corresponding measured high andlow-energy x-ray attenuations each define a height over the plane. Thereis thereby provided a first three-dimensional space for high-energyx-ray attenuation and second three-dimensional space low-energy x-rayattenuation. An example plane is shown in FIG. 5 wherein the high-energyand low-energy x-ray attenuations measured by a detector are representedon the z-axis, the path length values t₁ through the first material arerepresented on the x-axis and the path length values t₂ through thesecond material are represented on the y-axis. An examplethree-dimensional space is shown in FIG. 6 wherein the referencematerial path length values for each pixel representing the referencematerials define a plane as in FIG. 5, but wherein a z-axis alsorepresents the corresponding measured HE and LE x-ray attenuation forthat detector as a height off of the plane.

At step 320, a first mathematical model is selected which is a functionto collectively represent the measured high-energy x-ray attenuations ofat least one of the detectors and collectively represent the low-energyx-ray attenuations of the at least one of the detectors in terms of thematerial path length values t_(m) for each of the basis materials m=1,2. A suitable mathematical model can be selected to represent bothhigh-energy x-ray attenuations and low-energy x-ray attenuations, theonly difference being the value of the coefficients that best fithigh-energy x-ray attenuations and low-energy x-ray attenuations. Aninitial set of coefficients including at least one coefficient may thenbe selected for initializing the model for fitting the low-energy x-rayattenuations and the high-energy x-ray attenuations with the model. Thesets of coefficients may be identified using vector notation {rightarrow over (c)}^(E) where E=LE, HE represents the energy level of themeasured low and high-energy x-ray signals. The initial set ofcoefficients includes at least one coefficient which could potentiallybe applied to the model depending on the conditions of the scanningoperation.

A mathematical model such as, for example, a Pade's approximant would besuitable.

A set of fitting constraints may also be applied to the mathematicalmodel for selecting the coefficients reflecting the actual physicalbehavior of the direct attenuation surfaces. These constraints force allthe fitting coefficients to respect certain mathematical expressionsrepresenting real-world physics in order to assure that the inverseattenuation surfaces could be obtained and will be physicallymeaningful.

The data set representing the high and low-energy x-ray attenuationsÂ^(E)(t₁, t₂) may be fitted with the model A^(E)(t₁, t₂; {right arrowover (c)}^(E)) using an optimization algorithm as in step 322 and thefitting constraints to define the direct attenuation surfaces withintheir respective three-dimensional space as shown in steps 326 and 328,respectively. Fitted direct attenuation surfaces 800, 900 with datapoints used for the fitting for the LE and HE domains are shown,respectively, in FIGS. 8 and 9. The optimization algorithm determinesthe coefficients which provide the strongest correlation between themodel and the collective measured high and low-energy x-ray attenuationsiteratively starting with the selected initial set of coefficients. Thismay involve changes to the coefficients as the optimization algorithm isapplied until an optimum is reached and/or the coefficients stopschanging significantly. Such a determination of the coefficients may bemade on the basis of, for example, a least-squares analysis or any othersuitable method. Such a determination of the coefficients may also takeadvantage of known measurement uncertainties in dual-energy attenuationsand/or dual-material path length to weight the fitting points in asuitable way. In other words, the coefficients applied to the model arethose which provide the closest representation of all of the measuredhigh and low-energy x-ray attenuations collectively by the model in therespective three-dimensional space. The direct attenuation surface istherefore the representation or expression of the collective measuredhigh and low-energy x-ray attenuations provided by the model for therespective energy domain image. Such a representation may, for example,be a high-energy and a low-energy three-dimensional surface 600 relatedclosely to the measured high and low-energy x-ray attenuations as shownin FIG. 6.

The coefficients optimized for the model may be saved in a database asshown in step 324 to be used in further operations. This provides anadvantage whereby the potentially computationally intensive step ofdetermining the coefficients can be avoided.

An inverted three-dimensional space may then be defined for path lengthsof the first and the second material wherein the measured high andlow-energy x-ray attenuations define a second plane and the associatedpath lengths for the x-rays passing through the respective material eachdefine a height off of the second plane. At step 330, a second model isselected which is a function to collectively represent the firstreference material path lengths and second reference material pathlengths as a function of the associated low-energy x-ray attenuationsand high-energy x-ray attenuations to each define an invertedattenuation surface as shown in steps 332 and 334. Inverted attenuationsurfaces 1000, 1100 for each of t₁ and t₂ are shown, respectively, inFIGS. 10 and 11. As with the first mathematical model, a second set ofcoefficients including at least one second coefficient may be applied tothe second model for fitting the low-energy x-ray attenuations andhigh-energy x-ray attenuations with the second model. A second set offitting constraints including at least one second fitting constraint mayalso be applied to the second model for selecting the secondcoefficients. Once again, an optimization algorithm may be used, asshown in step 336, to determine the “best fit” second set ofcoefficients for fitting the low-energy x-ray attenuations andhigh-energy x-ray attenuations with the second model. From the invertedattenuation surfaces, the path lengths through each of the two referencematerials may be determined when an imposed low-energy x-ray attenuationvalue and high-energy x-ray attenuation value is imposed to the inverseattenuation surface. First and second reference material path lengthvalues associated with high and low-energy x-ray attenuation values maybe saved in lookup tables as shown in steps 308 and 310, respectively,for later reference, although the steps 308 and 310 are not necessarilyrequired for the purposes of the method described herein. The method mayalso totally avoid the use of the second model and determine numericallypointwise inverted surfaces using an optimization algorithm invertingthe attenuation surfaces, as shown in FIGS. 10 and 11. Alternatively, asecond model may be selected for expressing the pointwise invertedsurfaces as a function low-energy x-ray attenuation and the high-energyx-ray attenuation to define inverted attenuation surfaces.

It is preferable to first fit the first model with the firstcoefficients to define the direct attenuation surfaces and then providethe respective inverse attenuation surfaces within the invertedthree-dimensional space using the second mathematical model as describedabove since this is the more numerically accurate and physicallyinterpretable method of determining the “best fit” coefficients.However, it should be understood that in a second aspect, once themeasured low-energy and high-energy x-ray attenuations are associatedwith each of the first material path lengths and second material pathlengths as in the aforementioned method, the method may then proceeddirectly to the step of selecting the second model to collectivelyrepresent all of the first and second material path lengths asrespective heights off of the second plane to define the inverseattenuation surface. The second coefficients and the second set offitting constraints may be used with an optimization algorithm todetermine the coefficients directly for the inverted attenuationsurfaces without having to first define the direct attenuation surfaces.

There is thereby provided an association between the high-energy andlow-energy x-ray attenuation values provided by scanning first andsecond reference materials and corresponding first and second referencematerial path lengths. Using the aforementioned method, the materialpath lengths through each of the first and second reference materialsmay be determined when at least one low-energy and high-energy x-rayattenuation value is imposed to the inverted attenuation surface. Anypair of high-energy and low-energy x-ray attenuation values imposed onthe inverted attenuation surface corresponds to a single path lengthvalue through each of the first material and the second material. Thepath length information provided by the inverted attenuation surface maybe saved in an information database such as in a dual-material pathlength look-up table for use in future operations relating tocalibration or other operations whereby it would be useful to determinethe path length of basis materials directly from measured x-rayattenuation values in the high and/or low-energy image domains.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

Assignment of Z_(eff) to Reference Material Attenuation Information

The step 316 of effective atomic number lookup table generation isdiscussed in further detail with reference to FIG. 11. Once the firstand second reference material equivalent path lengths are associatedwith specific x-ray energy attenuation information provided by scanningthe reference materials, as in step 306, reference material equivalentpath lengths may be used to subsequently determine an appropriateeffective atomic number, or Z_(eff), to be assigned to the correspondingx-ray attenuation information.

If the contribution of scattered X-rays to the raw signals reaching adual-energy detector after having passed through a certain length of anhomogeneous material M (also called a path length) are neglected, and ifit is assumed that the density and atomic composition are constantthroughout the material, the dual-energy signal, preferably a normalizeddual-energy signal, may be evaluated by integrating a weightedtransmittance function of the material over the incident X-ray energy:I _(M) ^(E)(t _(M))=R∫ ₀ ^(∞) W ^(E)(E′)T _(M)(ρ_(M) ,t _(M) ,E′)dE′I_(M) ^(E) represents the X-ray signal intensity, R is a normalizationconstant, W^(E) is a weighting function, T_(M) us the transmittancefunction of the material M, E′ is the X-ray energy, t_(M) is the pathlength trough the material and ρ_(m) is the material mass density.

The weighting function used is energy dependent, and will therefore varydepending on the X-ray source and detectors used:

${W^{E}\left( E^{\prime} \right)} = \frac{E^{\prime}{D^{E}\left( E^{\prime} \right)}{S\left( E^{\prime} \right)}}{\int_{0}^{\infty}{E^{\prime}{D^{E}\left( E^{\prime} \right)}{S\left( E^{\prime} \right)}{dE}^{\prime}}}$Here, E′ represents the X-ray energy; S(E′) is the X-ray intensityspectrum emitted by the source that comes out of the belt in thescanner; D^(E) (E′) are the sensitivities of the dual-energy detectorsto X-rays of energy E′. One representation of the material transmittancefunction is:

${T_{M}\left( {\rho_{M},t_{M},E^{\prime}} \right)} = {\exp\left\lbrack {{- \rho_{M}}t_{M}\frac{\mu}{\rho_{M}}\left( E^{\prime} \right)} \right\rbrack}$The transmittance function of the material is an inverse exponentialfunction of the product of the mass density ρ_(m), the path length t_(M)and the mass attenuation

$\frac{\mu}{\rho_{m}}$of the material. The material transmittance is represented by T_(M) inthe above equation and the mass density of the material is representedby ρ_(m) in the above equation. The mass attenuation coefficient of amaterial is, according to the mixture rule, the weighted average of themass attenuation coefficients of the chemical elements composing thatmaterial. Therefore, one representation of the mixture rule may be:

${{\frac{\mu}{\rho_{M}}\left( E^{\prime} \right)} = {\Sigma_{i \in M}\mspace{11mu} w_{i}\frac{\mu}{\rho}\left( {Z_{i},E^{\prime}} \right)}},$where E′ represents the x-ray energy. The elements i in the material,represented by their atomic number Z_(i), are weighted by their weightfractions w_(i), or in other words, the product of the number of atomswith the atomic mass of each element divided by the total mass of themolecule of the material. Both the mass attenuation coefficient, whichmay be represented by μ/ρ (Z_(i), E′), and atomic masses, which may berepresented by A_(i), of various elements are available in atomicdatabases.

From an X-ray point of view, a material is totally described by itsenergy-dependent attenuation cross section per mol of electron andelectron density because these two properties completely encapsulate thex-ray absorption properties of a material. Therefore, to have physicalmeaning, the effective atomic number, Z_(eff), must be defined byspecifying the attenuation cross section of a material with a givenZ_(eff). For an element i, with an atomic number Z_(i), this may berepresented as:

${{\sigma_{e}\left( {Z_{i},E^{\prime}} \right)} = {\frac{\mu}{\rho}\left( {Z_{i},E^{\prime}} \right)\frac{A_{i}}{Z_{i}}}},$where σ_(e) is the energy-dependent attenuation cross section of anelement i with atomic number Z_(i). The energy-dependent attenuationcross section per mol of electron of an element is given by the productof the mass attenuation coefficient with the molar mass over the numberof electrons per (unionized) atom of that element, which also happens tobe the atomic number of that element.

Therefore, a first step to determining a Z_(eff)-dependent attenuationcross-section is to first determine an energy-dependent attenuationcross-section for a material M as shown in steps 338 and 340 for thefirst and second reference materials, respectively. In the context ofassigning effective atomic number values to the reference materials, thematerial M is one of the two reference materials. Accordingly, themethod described herein for assigning Z_(eff) values to x-ray signalenergy attenuation must be performed for each of the two referencematerials. The energy-dependent attenuation cross section for a materialM is given by the average of the energy-dependent attenuation crosssection per mol of electron of each element in that material, weightedby the total number of electrons of each element.

Then, the way to assign a Z_(eff) to a material that reproduces itscross section is to define a Z_(eff)-dependent cross section and to setthe Z_(eff) to the value that best fits the previously definedenergy-dependent attenuation cross section for a material M, as shown insteps 342 and 344 for each of the first and second reference materials,respectively. One suitable physics-based definition for theZ_(eff)-dependent cross section is a linear combination of the crosssections of the two elements Z_(i) and Z_(i+1) immediately adjacent tothe Z_(eff) value. This could be replaced by another model that fulfillsthe same purpose. However, if it is considered that the best Z_(eff)value is such that the Z_(eff)-dependent cross section is equivalent tothe energy-dependent attenuation cross section of a material, theeffective atomic numbers for each energy domain are fixed. In order todefine a single Z_(M) for material M, it is necessary to weight theenergy dependent curve of Z_(M) properly.

The evaluation of Z_(eff) is based on transmission measurements of apolychromatic X-ray spectrum emitted by the source through the materialof interest and other structural materials composing the scannerhousing. Thus, the weighting of the energy dependent Z_(eff) curve mustbe based on the transmission measurements of the incoming X-rayspectrum. The fraction of incoming X-ray of energy transmitted throughthe material, or simply the material transmittance, is an inverseexponential function of the electron density and the attenuation crosssection of material M. The electron density of material M is defined byits actual mass thickness and the weight fractions, atomic number andmass of each element that composes it. The mass thickness is defined asthe product of the mass density and the path length. An equivalentZ_(eff)-dependant material transmittance can be defined by using theZ_(eff)-dependent cross section instead of the energy-dependentattenuation cross-section, which closely resembles the actualenergy-dependent transmittance function of the material. This value isdetermined by minimizing the weighted squared transmission error, whichis given by integrating the weighted difference between the materialtransmission curve and the equivalent Z_(eff)-dependant materialtransmittance over the X-ray energy spectrum. Since the Z_(eff) isultimately determined using the total radiative energy transmittedthrough the material M and absorbed in the dual-energy detectors, theweighting is preferably a compromise between the dual-energy signalweighting, which complicates the error minimization procedure, butavoids ending up with two different Z_(eff) (one per energy level), andthe intensity spectrum weighting described in the publication K. Bond,J. Smith, J. Treuer, J. Azevedo, J. Kallman et H. Martz, «ZeCalcalgorithm details,» LLNL, Livermore, C A, 2013, which is hereinincorporated by reference in its entirety, that neglects the dependencyof Z_(eff) on the detection system.

Accordingly, the steps following the definition of the Z_(eff)-dependentcross-section for each energy level for each of the reference materialsinclude evaluating the energy-dependent material transmittance functionusing the previously defined energy-dependent attenuation cross-sectionfor each energy level, as shown in steps 346 and 348 for the first andsecond reference materials, respectively, and re-evaluating theenergy-dependent material transmittance function using theZ_(eff)-dependent cross-section as shown in steps 350 and 352 for eachof the first and second reference materials, respectively, to provide aZ_(eff)-dependent material transmittance function and a weighted squaredtransmission error as shown in steps 354 and 356. The weighted squaredtransmission error of the low-energy x-ray energy signal is thenminimized in steps 358 and 360 to assign a single Z_(eff) value to eachof the reference materials as shown in steps 362 and 364. It should beunderstood that the step of evaluating the energy-dependent materialtransmittance function using the previously defined energy-dependentattenuation cross-section for each energy level may be performed oncethe energy-dependent attenuation cross-section of each of the low-energyx-ray signal domain and the high-energy x-ray signal domain isdetermined.

It should be understood that the high-energy energy-spectrum-detectorweighting function or a combination of the low-energy and high-energyenergy-spectrum-detector weighting functions, could be used instead ofthe low-energy energy-spectrum-detector weighting function in order toprovide a single Z_(eff) value to be attributed to the high andlow-energy x-ray signal information provided by each of the tworeference materials.

The effective atomic number information may be stored in lookup tablesor in archive for use in other operations as in step 318 though this isnot necessarily required for the purposes of the method describedherein. This may avoid the need to execute this potentiallycomputationally intensive step in later operations wherein effectiveatomic number information may be used. Collectively, the effectiveatomic number values corresponding to a particular set of dual-energyattenuation images for the pair of reference materials may be referredto as the “effective atomic number images” or simply the “Z_(eff)images”.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

Assignment of Mass Thickness to Reference Material AttenuationInformation

The step 312 of mass thickness lookup table generation is discussed infurther detail with reference to FIG. 12. Once the path lengthinformation for the reference materials has been assigned to thedual-energy x-ray attenuation as in step 306, the path lengthinformation may be used as a basis for assigning mass thickness valuesto the dual-energy x-ray attenuation for each of the reference materialsas indicated in step 312. It should be noted that the determination ofmass thickness for the reference materials is not dependent on thedetermination of the Z_(eff) value for the reference materials in step312. Accordingly, the determination of mass thickness may be performedindependently of or in addition to the determination of Z_(eff) for thereference materials.

The dual-material decomposition approach includes rewriting the factorinside the aforementioned exponential function representing the materialtransmittance as a sum of two similar terms over the pair of referencematerials. So, the product of the mass thickness and the massattenuation of a material M is equivalent to the sum of the products ofthe mass density and mass attenuation coefficient of the first andsecond. The mass thickness of a material corresponds to the mass of thatmaterial by unit area seen by the detector. Since the source emitsX-rays radially, the area seen by the detector increases as the objectmoves toward the detector. This effect may be disregarded in the presentmethod. From a dual-material decomposition point-of-view, thedual-material mass thickness of a material M is defined as the sum ofthe mass thicknesses of the first and second reference materials.

In taking the above into consideration, the first step for assigningmass thickness values to the dual-energy x-ray attenuation informationincludes determining the mass density of each of the first and secondreference materials as shown in steps 366 and 368, respectively. Sincethe physical properties of each reference material are known, this stepmay, for example, be completed by retrieving the appropriate informationfrom a suitable source. The next step includes determining the first andsecond reference material equivalent path lengths. This may, forexample, be done prior to, subsequently to or in conjunction with steps366 and 368, using the method described above with reference to FIG. 3for assigning path length information to dual-energy attenuation valuesobtained by scanning each of the two reference materials as in step 306.The attenuation information may be imposed on an inverse attenuationsurface to identify the corresponding path lengths for each of the firstand second reference materials. Subsequently, a product of the firstmaterial equivalent path lengths and the mass density of the firstreference material is taken at step 370 to provide a first referencematerial mass thickness at step 372. Similarly, a product of the secondmaterial equivalent path lengths and the mass density of the secondreference material is taken at step 374 to provide a second referencematerial mass thickness at step 376. The first reference material massthickness and the second material mass thickness may then be summed atstep 378 to provide a total mass thickness of the first and secondreference materials at step 380.

As with the effective atomic number, the mass thickness valuesassociated with the dual-energy x-ray attenuation for each of thereference materials may be stored in lookup tables as in step 318 or inarchive for use in other operations, though this step is not requiredfor the purposes of the method as described herein. This may avoid theneed to execute this potentially computationally intensive step in lateroperations wherein mass thickness information may be used. Collectively,the mass thickness values corresponding to a particular set ofdual-energy attenuation images for the pair of reference materials maybe referred to as the “mass thickness images”.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

Assignment of Z_(eff) to Attenuation Information of Unknown Material

Once the effective atomic number Z_(m) of the two reference materialswith known atomic composition are known from step 316 and that the massthickness ρt_(m) has been defined as in step 314, these values and thedual-material equivalent path lengths t_(m) as determined in step 306may be used to determine the effective atomic number of a material Mwith an unknown composition. The reference material equivalent pathlengths, effective atomic numbers and mass thicknesses may be determineddirectly by way of new scans and determination according to the methodsdescribed above or may be retrieved from suitable lookup tables. This isfurther discussed with reference to FIG. 13.

If the mass thickness of a reference material that represents the dualmaterial composition of a material M is divided by the mass thickness ofthat material M, it is shown by involving the surface S of the detectorthat this is equivalent to the weight fraction of that basis material inthe dual material decomposition of the unknown material

$\frac{\rho_{m}t_{m}^{M}}{\rho\; t_{M}} = {\frac{S\;\rho_{m}t_{m}^{M}}{S\;\Sigma_{m}\rho_{m}t_{m}^{M}} = {\frac{\rho_{m}\left( {t_{m}^{M}S} \right)}{\Sigma_{m}{\rho_{m}\left( {t_{m}^{M}S} \right)}} = {\frac{\rho_{m}V_{m}^{M}}{\Sigma_{m}\rho_{m}V_{m}^{M}} = {\frac{m_{m}^{M}}{\Sigma_{m}m_{m}^{M}} = \omega_{m}^{M}}}}}$where V_(m) ^(M) and m_(m) ^(M) are effective volume and mass of basismaterial m in material M, respectively. Substituting the massthicknesses by weight fractions in the mass attenuation coefficientequation of the dual material decomposition, it becomes clear that thisis analogous to the mixture rule presented earlier, but this time in thecontext of the dual material decomposition. In other words,

${\frac{\mu}{\rho_{M}}\left( E^{\prime} \right)} \approx {{\left\lbrack \frac{\rho_{1}t_{1}^{M}}{\rho\; t_{M}} \right\rbrack\frac{\mu}{\rho_{1}}\left( E^{\prime} \right)} + {\left\lbrack \frac{\rho_{2}t_{2}^{M}}{\rho\; t_{M}} \right\rbrack\frac{\mu}{\rho_{2}}\left( E^{\prime} \right)}}$becomes${\frac{\mu}{\rho_{M}}\left( E^{\prime} \right)} \approx {{\omega_{1}^{M}\frac{\mu}{\rho_{1}}\left( E^{\prime} \right)} + {\omega_{2}^{M}\frac{\mu}{\rho_{M}}\left( E^{\prime} \right)}}$Taking the mixture rule into consideration, this is equivalent to saythat the material M is made of a combination of the basis materials,just as it was previously defined in the mixture rule as being composedof a combination of different chemical elements.

The Z_(eff) of various materials are not necessarily positive integervalues, like the atomic number of chemical elements. Instead, they maketake any positive real values. When the Z_(eff) of a material is equalto an integer value, the mass attenuation coefficient must be equal tothe mass attenuation coefficient of the element that has an atomicnumber equal to that integer value. The behaviour of the massattenuation coefficient for non-integer Z_(eff) is provided by theaforementioned model. Of note, when the Z_(eff) is equal to one of thetwo reference materials, it can be expected that the mass attenuationcoefficient is the same as the mass attenuation coefficient of thatreference material. When a material M is decomposed into referencematerials (from the dual material decomposition), it can be furtherassumed that the reference materials could be further decomposed intotheir chemical elements (since their chemical composition should be wellknown). This concept is used to determine the weight fraction of eachbasis element j of the first and second reference materials:

$\varpi_{j}^{M} = \left\{ \begin{matrix}{{\sum\limits_{m}{\omega_{m}^{M}w_{j \in m}}},} & {{{if}\mspace{14mu} j\mspace{14mu}{is}\mspace{14mu}{present}\mspace{14mu}{in}\mspace{14mu} m} = {{1\mspace{14mu}{or}\mspace{14mu} m} = 2}} \\{\mspace{115mu}{0,}} & {{otherwise}\mspace{259mu}}\end{matrix} \right.$This effective basis element weight fraction can be used to determinethe mass attenuation coefficient for the unknown material, just like itwas used for the reference materials.

Accordingly, the method for assigning an effective atomic number to anunknown material begins at step 1300 with the scanning of an unknownmaterial in an x-ray scanning device to obtain dual-energy x-rayattenuation information for the unknown material at step 1302. Thedual-energy x-ray attenuation information of the unknown material maythen be imposed to the inverted attenuation surface at step 1304, orreferenced using a suitable lookup table, to determine equivalent firstand second reference material path lengths through the unknown materialas shown in steps 1306 and 1308. It should be understood thatcorresponding first and second reference material equivalent pathlengths may be retrieved from suitable lookup tables as provided bysteps 308 and 310 of FIG. 3, if stored in archive subsequent to a priorcalibration method scanning operation. The first and second referencematerial mass thickness in the unknown material may then be determinedat steps 1310 and 1312, respectively, using the equivalent first andsecond reference material path lengths and known mass density of thefirst and second reference materials. A total mass thickness of theunknown object may be determined as in step 1314 based on a sum of themass thickness of each of the first and second reference materials inthe unknown material. As shown in step 1316, the unknown object totalmass thickness may be divided by the unknown object path lengths throughthe unknown object to provide the mass density of the unknown object atstep 1318.

In the next step 1320, a first weight fraction of each of the first andsecond reference materials in the unknown material may be determined. Asecond weight fraction of each basis element of each of the first andsecond reference materials in the unknown material is also determined atstep 1322. A mass attenuation coefficient for the unknown material isdetermined at step 1324, with a product of the effective weight fractionof each basis element of each of the first and second material in theunknown third material and the mass attenuation coefficient of thecorresponding element in the first and second materials. The methodfurther includes at step 1326 determining an attenuation cross sectionof the unknown object. This may be accomplished, for example, by usingthe respective known basic atomic properties such as the respectiveeffective atomic masses and atomic numbers and mass attenuationcoefficient for each of the first and second material.

Then a procedure similar to the one used to assign an effective atomicnumber to the reference materials is used for the unknown material.Following the determination of the mass attenuation coefficient for theunknown material at step 1326, this includes the steps of defining aZeff-dependent attenuation cross-section as shown in step 1328,evaluating the energy-dependent material transmittance function at step1330 using the previously defined energy-dependent attenuationcross-section for each energy level and re-evaluating theenergy-dependent material transmittance function at step 1332 using theZ_(eff)-dependent cross-section to provide at steps 1334 and 1336,respectively, a Z_(eff)-dependent material transmittance function and aweighted squared transmission error for each energy level. The weightedsquared transmission error of each energy level and preferably thelow-energy x-ray energy signal is then minimized at steps 1338 and 1340,respectively, to assign a single Z_(eff) value to the unknown materialat step 1342. It should be understood that, as with the aforementionedmethod as described within the context of assignment of effective atomicnumber values to the first and second reference materials, the step 1332of evaluating the energy-dependent material transmittance function usingthe previously defined energy-dependent attenuation cross-section foreach energy level may be performed once the energy-dependent attenuationcross-section of each of the low-energy x-ray signal domain and thehigh-energy x-ray signal domain is determined. Accordingly, steps 1332and 1328, wherein the Z_(eff)-dependent attenuation cross-section isdefined, are interchangeable.

Note that this procedure does not actually depend on Z_(m) for m=1, 2,but rather on the decomposition of the fictitious material on adual-material element basis. Thus, the Z_(eff) is calculated with onlyone additional approximation than Z_(m), i.e.: the generalized massattenuation coefficient of fictitious material M can be represented by alinear combination of the basis elements j of which the first and secondreference material are actually made of. This method is a “multi-elementdual-material decomposition” for the effective atomic numbercalculation.

Alternatively, instead of repeating the above process every time a newmaterial is scanned, this procedure can also be done in advance for allpoints (I^(LE)/I^(HE)) in the dual-energy signal mesh. This generates,point by point, the effective atomic number surface Z_(eff)(I^(LE),I^(HE)) and associated uncertainties. Also, if a reverse modelassociating attenuations to path lengths was used, a new set ofcoefficients {right arrow over (f)}, associated with the effectiveatomic number, has to be derived from the model selected and thedefinition of the effective atomic number adopted. Then theZ_(eff)(I^(LE), I^(HE)) of the set of coefficients {right arrow over(f)} is saved in an effective atomic number database.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

Background Removal Method

Reference material path length decomposition also allows for a set ofdual energy images or image archives to be transformed into a new set ofdual energy images or image archives with layers of materials removed.Depending on the shape and nature of the materials removed, this canlead to images where contrast between objects is enhanced, or whereobjects are completely removed from the image. This is done byappropriately subtracting the mass thickness of the material or objectto be removed from the mass thickness of the combined objects in thearchive. Usually, the object to be removed is in the background of theobject that is of main interest. Different methods are used to properlyevaluate the mass thickness of the background material or object,depending on its shape and whether prior knowledge of it is available.

In some instances, the background to be removed is already known to theX-ray scanner operators. In such cases, the background will have beenscanned previously and preferably, the dual-energy images are availablein archive. One example of a background object which may be known to anX-ray scanner operator and may have been previously scanned would be astandard x-ray screening tray. Preferably, the tray will have beenscanned in the x-ray scanning device in various positions andorientations to provide a plurality of dual-energy images of thescreening tray which would be available for subsequent operations fromarchive. In these cases, a particular method can be used to remove thebackground object from a newly scanned dual-energy image representingx-ray signal information of the background object and an object ofinterest at least partially overlapping with one another.

In accordance with one aspect, there is provided a method for assigningan attribute to an object of interest overlapping with a predeterminedbackground object as shown in FIG. 14. The method includes firstscanning the predetermined background object in a plurality of positionsand orientations within an x-ray scanning device at step 1400 to obtaina plurality of first dual-energy attenuation images at step 1402 eachhaving dual-energy attenuation information representing the scannedbackground object. This scanning step 1400 can be performed offline,prior to performing a scan including an object of interest. Then, thebackground object dual-energy attenuation images may then be decomposedinto background object dual-reference material equivalent path lengthimages having first and second reference material equivalent pathlengths passing through the background object at step 1404. Suchdecomposition may be performed, for example, using suitable lookuptables or by way of the method described above with reference to FIG. 3.Thereby, there is provided a reference material equivalent path lengthimages of the predetermined background object at step 1406.

In the next step 1408, the unknown object at least partially overlappingwith the background object may be scanned within the x-ray scanningdevice to obtain a second set of dual-energy attenuation images at step1410 each having dual-energy attenuation information representing anoverlap region wherein the background object and the unknown objectoverlap. Such an image is illustrated in FIG. 15, for example, whereinx-ray path lengths 1500 are shown passing through both the backgroundobject 1502 and the unknown object of interest 1504. Some of the x-raypath lengths pass through both of the background object 1502 and theunknown object of interest 1504 thereby creating an “overlap region”1506 within the image which overlap region is delineated by imaginarydashed lines 1508.

The second set of dual-energy attenuation images may then be decomposedat step 1412 into reference material equivalent path length imagesprovided at steps 1414, wherein the overlap region has first and secondreference material equivalent path lengths passing through both thebackground object and the unknown object. The position and orientationof the background object in the reference material equivalent pathlength images containing the overlap region is then determined at step1416, preferably by using a segmentation algorithm to localize thebackground object as shown in step 1418. It should be understood thatthe segmentation algorithm may be applied to either one of thedual-energy attenuation images or the reference material path lengthimages to localize the background object. Accordingly, the segmentationalgorithm may instead be applied to the images provided at step 1410, asshown in step 1430. Then, at step 1420, the position and orientation ofthe background object as identified by the segmentation algorithm iscompared with the reference material path length images of thepredetermined background object to determine corresponding ones of thereference material equivalent path length images of the predeterminedbackground object which most closely corresponds with the position andorientation of the background object in the reference materialequivalent path length images of the scanned unknown object with theoverlap region. Once this determination is made, the predeterminedbackground object reference material equivalent path lengths of thecorresponding ones of the plurality of the predetermined backgroundobject reference material equivalent path length images may beeliminated or subtracted from the overlap region in the referencematerial equivalent path length images of the unknown object at step1422 to provide reference material equivalent path lengths having firstand second reference material equivalent path lengths passing throughonly the unknown object, as shown in step 1424. There is therebyprovided background-free first reference material equivalent path lengthimages.

Decomposition of the dual-energy attenuation images of the predeterminedbackground object at step 1404 or the dual-energy attenuation imagesrepresenting the scanned unknown object at step 1412 into referencematerial equivalent path lengths may be performed in any mannerpreviously described, such as for example, by imposing the dual-energyattenuation information of each pixel onto the inverse attenuationsurface to obtain the first and second equivalent reference materialpath lengths or by using suitable lookup tables. This is previouslydiscussed with reference to FIGS. 3 and 11 and in particular step 306shown in FIG. 11.

Once the background object-free reference material equivalent pathlength images are provided at step 1424, the corresponding backgroundobject-free dual-energy attenuation images may be reconstructed. This isdone, for example, by imposing, at step 1426, the reference materialpath length values onto a suitable direct attenuation surfaces, asdescribed above, to obtain the corresponding high-energy and low-energyattenuation information images at steps 1428. Once the backgroundobject-free dual-energy attenuation images are provided, the images maybe normalized. This is previously discussed with reference to FIGS. 3and 11 and in particular step 306 shown in FIG. 11. These images canfurther be used to determine the physical characteristics (such as massthickness and effective atomic number) of the objects remaining, suchas, for example, by way of the assignment of the effective atomic numberand mass thickness to an unknown material discussed above.

In another aspect, the background object to be removed is not known bythe operators but has or is determined to have a path lengthdistribution that is uniform. Preferably, the uniform path lengthdistribution is in the direction of the belt since in the image, thiscorresponds to the horizontal direction. Under such circumstances, asecond method may be used to effectively remove the background objectfrom the image. This method uses a region in the image where only thebackground object to be removed is present and there are no otherobjects or materials overlapping with the background object. Since thebackground is not known but has a uniform path length distribution,preferably in the horizontal direction, the background object must bethe same thickness in background only areas and in areas overlappingwith other objects. These conditions are understood to be true for eachrow of pixels in the image in which the background object must beremoved, since each row in the image corresponds to a different ray fromthe X-ray fan beam. To simplify, the background object path length isevaluated in a pixel in a background only region, and since, based onthe above conditions, it can be safely assumed to be the same in allother pixels of the same row of pixels, then the background object pathlengths can be removed, even if the background object itself is unknown.

There is provided a method as shown in FIG. 16 for assigning anattribute to an unknown object overlapping with an unknown backgroundobject having homogenous composition and thickness. In the first step1600, the unknown object at least partially overlapping with thebackground object is scanned within the x-ray scanning device to obtaina dual-energy attenuation images at step 1602 having pixels distributedin rows and columns and each having dual-energy attenuation information.The dual-energy attenuation images are then decomposed at step 1604 intodual-reference material equivalent path length images provided at step1606, each dual-reference material equivalent path length image having abackground region with first and reference material equivalent pathlengths passing through only the background object and an overlap regionwith first and second reference material equivalent path lengths passingthrough the unknown object of interest overlapping with the backgroundobject. The background region and the overlap region are then determinedat step 1608 by using a segmentation algorithm at step 1610 to localizethe background region within the dual-reference material path lengthimages of the unknown object. It should be understood that thesegmentation algorithm may be applied to either one of the dual-energyattenuation images or the reference material path length images tolocalize the background object. Accordingly, the segmentation algorithmmay instead be applied to the images provided at step 1602, as shown instep 1630. Then, at step 1612, one of an average, a median and a mean,preferably the average, of the first and second reference materialequivalent path lengths passing through only the background object ineach column is determined. At step 1614, the one of the average, themedian and the mean of the first and second reference materialequivalent path lengths passing through only the background object ineach column is eliminated or subtracted from the first second referencematerial equivalent path lengths of each column of the overlap region todetermine reference material equivalent path lengths representing onlythe unknown object of interest as shown at step 1616.

Once the background object-free reference material equivalent pathlength images are provided at step 1616, the corresponding backgroundobject-free dual-energy attenuation images may be reconstructed. This isdone, for example, by imposing, at step 1618, the reference materialpath length values onto a suitable direct attenuation surfaces, asdescribed above, to obtain the corresponding high-energy and low-energyattenuation information images at steps 1620. Once the backgroundobject-free dual-energy attenuation images are provided, the images maybe normalized. This is previously discussed with reference to FIGS. 3and 11 and in particular step 306 shown in FIG. 11. These images canfurther be used to determine the physical characteristics (such as massthickness and effective atomic number) of the objects remaining, suchas, for example, by way of the assignment of the effective atomic numberand mass thickness to an unknown material discussed above.

Even when no prior information about the background object is known andthe background object is not horizontally uniform, there is provided athird method to perform background object removal. Once again, themethod uses, in addition to regions of overlap of the background andanother object in the image, a region where there is only backgroundobject. The background object path lengths are known and may bedetermined using measurements or determined by way of a reconstructionalgorithm or any other suitable method. The mass density and averageatomic effective atomic number of the background object must be constantthroughout the background object, both in the background-only region andoverlap region of the image. Likewise, both the mass density andeffective atomic number of the reference materials from thedual-material decomposition must be known. Finally, the effective atomicmodel referred to earlier must be mathematically invertible.

In another aspect, there is therefor provided a method for assigning anattribute to an object of interest overlapping with a background objecthaving homogenous composition and non-uniform known thickness. In afirst step 1700, the unknown object at least partially overlapping withthe background object is scanned within the x-ray scanning device toobtain a dual-energy attenuation images at step 1702 each having pixelsdistributed in rows and columns and having dual-energy attenuationinformation. The dual-energy attenuation images are decomposed at step1704 into reference material equivalent path length images, provided atstep 1706, having a background region with first and second referencematerial equivalent path lengths passing through only the backgroundobject and an overlap region with first and second reference materialequivalent path lengths passing through the unknown object of interestoverlapping with the background object. The effective atomic number ofeach pixel of the dual-reference material equivalent path length imagesis determined at step 1708 and the mass thickness of each pixel of thebackground region and the overlap region in the dual-reference materialequivalent path length images is also determined at step 1710. In thenext step 1712, the background region and the overlap region arelocalized, preferably by using a segmentation algorithm as shown at step1714. It should be understood that the segmentation algorithm may beapplied to either one of the dual-energy attenuation images or thereference material path length images to localize the background object.Accordingly, the segmentation algorithm may instead be applied to theimages provided at step 1702, as shown in step 1740. Then, the pathlengths passing through the background object are obtained or determinedusing suitable methods at step 1716. The mass thickness of each pixel ofthe background region may be divided, as at step 1718 by the knownbackground object path lengths to determine the mass density of eachpixel of the background region as shown at step 1720. At step 1722, oneof an average, a median and a mean of the effective atomic number andthe mass density across all pixels of the background region isdetermined. At step 1724, for every pixel in the overlap region, themass density of the background region is multiplied with the pathlengths of the background region. Next, at step 1726, for every pixel inthe overlap region, the mass thickness of the background region iseliminated or subtracted from the total mass thickness of the backgroundregion and the overlap region to provide an unknown object massthickness at step 1728. Next, the density of the unknown object isdetermined. For every pixel in the overlap region, the unknown objectmass thickness is divided by the path length through the unknown objectto provide the density of the unknown object at step 1730. Once the massdensity is provided at step 1730, the effective atomic number of theobject is also calculated as shown at step 1732.

The effective atomic number of the object of interest is calculated byisolating the object effective atomic number in an equation that linksthe total mass thickness and effective atomic number values of everypixel with those of the object of interest and background object in theoverlap region:g[Z _(eff)(i,j)]ρt(i,j)=g[Z _(o)]ρ_(o) t _(o)(i,j)+g[Z _(b)]ρ_(b) t_(b)(i,j)where; Z is the effective atomic number of every pixel in the object andbackground in the overlap region, where g[Z] is an invertible functionof Z, where o and b represent the object and background respectively,where ρt is the mass thickness, and where i and j represent the pixel ofthe i^(th) row and j^(th) column. Isolating the effective atomic numberof the object Z_(o) gives:

${Z_{o}\left( {i,j} \right)} = {g^{- 1}{\left\{ \frac{{{g\left\lbrack {Z_{eff}\left( {i,j} \right)} \right\rbrack}\rho\;{t\left( {i,j} \right)}} - {{g\left\lbrack {\overset{\_}{Z}}_{b} \right\rbrack}\rho\;{t_{b \in {ob}}\left( {i,j} \right)}}}{\rho\;{t_{o \in {ob}}\left( {i,j} \right)}} \right\}.}}$The background-free dual-material path lengths images of the object t₁^(o)(i,j) and t₂ ^(o) (i, j) are then determined at step 1734 by solvingthe following system of equation for every pixel (i, j) in the overlapregion ob:

$\left\{ {\begin{matrix}{{\rho\;{t_{o \in {ob}}\left( {i,j} \right)}} = {{\rho_{1}{t_{1}^{o}\left( {i,j} \right)}} + {\rho_{2}{t_{2}^{o}\left( {i,j} \right)}}}} \\{{{g\left\lbrack {Z_{o}\left( {i,j} \right)} \right\rbrack}\rho\;{t_{o \in {ob}}\left( {i,j} \right)}} = {{{g\left\lbrack Z_{1} \right\rbrack}\rho_{1}{t_{1}^{o}\left( {i,j} \right)}} + {{g\left\lbrack Z_{2} \right\rbrack}\rho_{2}{t_{2}^{o}\left( {i,j} \right)}}}}\end{matrix}\quad} \right.$wherein the solutions are:

${t_{1}^{o}\left( {i,j} \right)} = {\frac{\rho\;{t_{o \in {ob}}\left( {i,j} \right)}}{\rho_{1}}\left\{ \frac{{g\left\lbrack {Z_{o}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{2} \right\rbrack}}{{g\left\lbrack Z_{1} \right\rbrack} - {g\left\lbrack Z_{2} \right\rbrack}} \right\}}$${t_{2}^{o}\left( {i,j} \right)} = {\frac{\rho\;{t_{o \in {ob}}\left( {i,j} \right)}}{\rho_{2}}{\left\{ \frac{{g\left\lbrack Z_{1} \right\rbrack} - {g\left\lbrack {Z_{o}\left( {i,j} \right)} \right\rbrack}}{{g\left\lbrack Z_{1} \right\rbrack} - {g\left\lbrack Z_{2} \right\rbrack}} \right\}.}}$Decomposition of the dual-energy attenuation images of the backgroundobject at step 1704 may be performed in any manner previously described,such as for example, by imposing the dual-energy attenuation informationof each pixel onto the inverse attenuation surface to obtain the firstand second equivalent reference material path lengths or by usingsuitable lookup tables. This is previously discussed with reference toFIGS. 3 and 11 and in particular step 306 shown in FIG. 11.

Once the background object-free reference material equivalent pathlength images are provided at step 1734, the corresponding backgroundobject-free dual-energy attenuation images may be reconstructed. This isdone, for example, by imposing, at step 1736, the reference materialpath length values onto a suitable direct attenuation surfaces, asdescribed above, to obtain the corresponding high-energy and low-energyattenuation information images at steps 1738. Once the backgroundobject-free dual-energy attenuation images are provided, the images maybe normalized. This is previously discussed with reference to FIGS. 3and 11 and in particular step 306 shown in FIG. 11. These images canfurther be used to determine the physical characteristics (such as massthickness and effective atomic number) of the objects remaining, suchas, for example, by way of the assignment of the effective atomic numberand mass thickness to an unknown material discussed above.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

Calibration Range Extension Method

The dual material decomposition described above in the calibrationmethod is best suited for the range of effective atomic numbers situatedbetween the effective atomic numbers of the reference materials used inthe calibration step wedges. It may be desirable to extend thecalibration range provided by a standard dual-material calibrationmethod while keeping the physical significance of inverse attenuationsurfaces generated using the calibration method. This would enabledual-material decomposition of a wider range of material compositionsthan would be possible for a given set of two reference materials with astandard dual-material calibration method.

In a first method, two or more of the ranges of the dual-material pathlength decomposition data may be combined to extend the total range ofdual-material path length decomposition data. In this first method,dual-material path length decomposition is performed on a firstreference material and a second reference material. Then, dual-materialpath length decomposition is performed on the second reference materialwith a third reference material. Therefore, the second referencematerial path attenuation information is common to both sets of data. Asubset of coefficients is then identified which may be used to combinethe dual-material decomposition information provided by the first andsecond reference material ({right arrow over (c)}₁₂ ^(E)) and the secondand third reference material ({right arrow over (c)}₂₃ ^(E)) based onthe common elements of the models used to represent the second referencematerial within the two data sets. Thereby, a broader range ofattributes may be assigned to x-ray attenuation values.

With reference to FIG. 18, in a first aspect, the method for assigningattributes to x-ray attenuation information includes as a first step1800 acquiring first and second reference material equivalent pathlength information associated with a first range of dual-energy x-rayattenuation information. At step 1802, second and third referencematerial equivalent path length information associated with a secondrange of dual-energy x-ray attenuation information is acquired. At step1804, suitable coefficients are determined for representing thedual-energy x-ray attenuation information of the second referencematerial. At step 1806, the coefficients are used to join the first andsecond dual-energy x-ray attenuation information ranges to define, atstep 1808, a third dual-energy x-ray attenuation information range uponwhich upon which may be imposed dual-energy x-ray attenuation valueswithin the third dual-energy x-ray attenuation information range todetermine corresponding first reference material equivalent path lengthsand third reference material equivalent path lengths.

The first and second reference material equivalent path lengthinformation and second and third reference material equivalent pathlength information may be determined by any suitable method previouslydescribed. Preferably, such information is retrieved from lookup tables,as shown at step 1810, having, respectively, saved first and second orsecond and third reference material equivalent path lengths associatedwith the dual-energy x-ray attenuation information corresponding withthe dual-energy attenuation information range. Alternatively, as shownat step 1812, the first and second or second and third referencematerial path length information may be determined by repeating thedual-material decomposition method previously described for fresh scansof suitable reference materials.

In another method, the calibration range may be extended using a singleadditional material. When decomposed onto the dual-material basis offirst and second reference materials, dual-energy attenuation curves ofthe second reference material may be represented by A₁₂ ^(E)(0, t₂;{right arrow over (c)}₁₂ ^(E)).

If it is further considered that a decomposition onto the dual-materialbasis of the first reference material and a third reference material,with the effective atomic number of the third reference material beinggreater than the effective atomic number of the second referencematerial and the effective atomic number of the second referencematerial being greater than the effective atomic number of the firstreference material, and the associated dual-energy direct attenuationsurfaces of the first and third reference material and correspondingcoefficients of the third reference material, then it is understood thatthe second reference material would be represented by a subset of datain the range of the first reference material and the third referencematerial. This concept is illustrated in FIG. 19 wherein the rangeprovided by the first reference material and the third referencematerial is represented by the first quadrant in a graph. The secondreference material is represented by a specific radial axis coming outof the origin in the first quadrant of the t₁-t₃ plane. If the inverseattenuation surfaces for the first and third reference materials areavailable, then all the pixels of the first and third reference materialpath length images of an object made of the second reference materialwould fall on this axis, no matter the path length through the secondreference material.

Denoting the slope of the line supporting the axis representing thesecond reference material in the t₁-t₃ plane by ω₂, the line equationmay be represented by:t ₃=ω₂ t ₁

The orientation of this line can also be defined by the volume fractionof the first reference material in the dual-material basis of the firstand third reference materials representing the second reference materialthis may be represented by:

$v_{2} = {\frac{1}{1 + \omega_{2}} = \frac{t_{1}}{t_{1} + t_{3}}}$

The sum of the first and third reference materials path lengths on theaxis representing the second reference material may be represented by:s ₂ =t ₁ +t ₃

Since t₁, t₃≥0 in the first quadrant, s₂≥0 and s=0 if and only ift₁=t₃=0 (i.e. at origin) Then, the change of variables (t₁, t₃)→(s₂, ν₂)can be defined using the set of equations:

$\left\{ {\begin{matrix}{{{t_{1}\left( {s_{2},v_{2}} \right)} = {v_{2}s_{2}}}\mspace{56mu}} \\{{t_{3}\left( {s_{2},v_{2}} \right)} = {\left( {1 - v_{2}} \right)s_{2}}}\end{matrix}\quad} \right.$

The dual-energy attenuation curves over the axis representing the secondreference material in the dual-material basis provided by the first andthird reference materials may therefore be represented as A₁₃ ^(E) (s₂,ν₂; {right arrow over (c)}₁₃ ^(E)) for s≠0. For s=0, it is clear thatattenuations vanish for both the high and low energy level. By thereunion of the domains (s₂=0 and s₂≠0), then A₁₃ ^(E) (s₂, ν₂; {rightarrow over (c)}₁₃ ^(E)) is defined over the domain s₂≥0.

For fixed ν₂ and dual-energy attenuations that could be both achievedfor a given path length t₂ through the second reference material, itshould be understood that in general: t₂≠s₂. However, there is anonlinear path length-dependent scaling factor S₂ (t₂) mapping locallyA₁₂ ^(E)(0, t₀; {right arrow over (c)}₁₂ ^(E)) onto A₁₃ ^(E) (S₀, ν₂;{right arrow over (c)}₁₂ ^(E)) for some s₀=S₂ (t₀). The union of allsuch mappings along the axis representing the second reference materialin the dual-material decomposition of the first and third referencematerial plane leads to a continuous function s₂=S₂(t₂). Physically, wealso know that S₂ (0)=0.

Therefore, in order to extend the calibration range provided by thedual-material decomposition of the first and second reference materialup to a calibration range provided by the dual-material decomposition ofthe first and third reference material without having to first determinethe direct or inverse attenuation surfaces of the dual-material basisprovided by the first and third reference materials, it is desired todetermine the map S₂ between t₂ and s₂, the dual-material basis providedby the first and third reference materials and the orientation ν₂ of theaxis representing the second reference material in the first and thirdreference material dual-material basis.

It can be assumed that there is an orientation and a scaling factor suchthat:

A₁₂ ^(E)(0, t₂; {right arrow over (c)}₁₂ ^(E))=A₁₃ ^(E)(S₂(t₂), ν₂;{right arrow over (c)}₁₃ ^(E)) all over the s₂ axis. Thus, using thisequivalence principle and knowing that A₁₂ ^(E) (0, t₂; {right arrowover (c)}₁₂ ^(E)) explicitly, the mapping S₂(t₂) can be found implicitlyfor fixed ν₂. ν₂ can be determined because the above equation holds truewhen t₂=s₂=0.

In accordance with the above and with reference to FIG. 20, a secondaspect of the method for assigning an attribute to x-ray attenuationincludes acquiring at step 2000, first and second reference materialequivalent path length information associated with a first range ofdual-energy x-ray attenuation information by a first model forexpressing collectively each of the first reference material pathlengths and the second reference material path lengths as a function ofthe associated first range of dual-energy x-ray attenuation information.The first range of dual-energy attenuation information is fitted withthe first model by a first set of coefficients. At step 2002, the firstset of coefficients is determined. At step 2004, there is acquired thirdreference material equivalent path length information associated with asecond range of dual-energy x-ray attenuation information by a secondmodel for expressing collectively each of the third reference materialequivalent path lengths as a function of the associated second range ofdual-energy attenuation information. The second range of dual-energyattenuation information is fitted with the second model by a second setof coefficients. At step 2006, the second set of coefficients isdetermined. The third reference material has an effective atomic numbergreater than that of the second reference material. At step 2008, thefirst set of coefficients and the second set of coefficients arecombined to provide a third set of coefficients at step 2010 for fittingthe first and second range of dual-energy x-ray attenuation informationwith a third model for expressing collectively the first and thirdreference material path lengths as a function of the fitted first andsecond range of dual-energy x-ray attenuation information. For allpoints in the third model, there is determined at step 2012, a volumefraction of one of the first and the third reference material whichrepresents the second reference material path lengths to identify wherein the third model path lengths representing the second referencematerial are represented. There is thereby provided at step 2014 thethird dual-energy x-ray attenuation range.

The first and second reference material equivalent path lengthinformation and third reference material equivalent path lengthinformation may be determined by any suitable method previouslydescribed. Preferably, such information is retrieved from lookup tables,as shown at steps 2016 and 2018, having, respectively, saved first andsecond or third reference material equivalent path lengths associatedwith the dual-energy x-ray attenuation information corresponding withthe dual-energy attenuation information range. Alternatively, as shownat steps 2020 and 2022, the first and second or third reference materialpath length information may be determined by repeating the dual-materialdecomposition method previously described for fresh scans of suitablereference materials.

With reference to FIGS. 21 and 22, there is provided, in a third aspect,a method for extending the calibration range provided by a first andsecond reference material beyond the effective atomic number range ofthe reference materials. Direct attenuation surfaces fitted on thecalibration data for the first and second reference materialdual-material decomposition basis, shown in the first quadrant of FIG.22 are also valid in regions of the second and fourth quadrants near theaxis representing the first reference material path lengths (t₁-axis)and the second reference material path lengths (t₂-axis), respectively,This is equivalent to extending the first reference material pathlengths t₁ or the second reference material path lengths t₂ to slightlynegative values while the other remains positive. Negative path lengthsrepresent an imposed or fictitious amount of a reference material thatwould have to be added to the dual-material images of the scanned objectfor the effective atomic number of the composite object (original objectplus the added negative layer) to provide a reference material pathlength that would result in finding an effective atomic number equal tothat of the actual reference material.

However, in order to provide more accurate and useful data, thisextrapolation must be constrained to predetermined minimum and maximumeffective atomic numbers for the imposed materials making up thenegative path lengths. Preferably, this minimum effective atomic numberis approximately equal to or greater than 3 and the maximum effectiveatomic number is approximately equal to or less than 42.

In this third aspect, there is provided a method for assigning anattribute to x-ray attenuation. In a first step 2100, there is acquiredfirst and second reference material equivalent path length informationassociated with a first range of dual-energy x-ray attenuationinformation by a model for expressing collectively each of the firstreference material path lengths and the second reference material pathlengths as a function of the associated first range of dual-energy x-rayattenuation information. At step 2102, an extrapolation range ofdual-energy x-ray attenuation information is selected over which firstand second reference material path lengths are to be associated withdual-energy x-ray attenuation information of a first imposed materialhaving a predetermined minimum effective atomic number less than aneffective atomic number of the first reference material and a secondimposed material having a predetermined maximum effective atomic numbergreater than an effective atomic number of the second referencematerial. The first range is within the extrapolation range. At step2104, a set of fitting constraints is selected for associating each ofthe first reference material path lengths and the second referencematerial path lengths over the extrapolation range of dual-energyattenuation information. At step 2106, the set of fitting constraintsare applied to the model to define at step 2108 extrapolated first andsecond reference material equivalent path lengths over the extrapolationrange.

The first and second reference material equivalent path lengthinformation may be determined by any suitable method previouslydescribed. Preferably, such information is retrieved from lookup tables,as shown at step 2110, having therein saved first and second referencematerial equivalent path lengths associated with the dual-energy x-rayattenuation information corresponding with the dual-energy attenuationinformation range. Alternatively, as shown at step 2112, the first andsecond reference material path length information may be determined byrepeating the dual-material decomposition method previously describedfor fresh scans of suitable reference materials.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

Object Reconstruction Method

There is also provided a method to find the density and effective atomicnumber Z_(eff) of objects present in scanned images. This isparticularly useful in the context of identification of LAG(liquid-aerosol-gel) materials which may be contained within a containerat the time of scanning.

With reference to FIGS. 23A and 23B, in a first aspect, the method forassigning attributes to an object of interest may be described asfollows. However, it should be understood that certain steps in themethod may be performed by different means, depending on the conditionsrelating to the object of interest that is scanned without departingfrom the scope of the invention described herein. Certain steps may alsobe performed in a different order than that presented in the followingdescription.

In a first step 2300, the unknown object of interest is scanned.Typically, the object of interest at least partially overlaps with abackground object within an x-ray scanning device, such as, for example,a security screening tray. The unknown object may also be containedwithin a container that is placed within the tray for the scanningoperation. The x-ray scanning device emits x-rays from at least twosources which pass through the unknown object and the background objectto be detected by at least one array of detectors. The detectors provideat step 2302 a plurality of dual-energy attenuation images each havingdual-energy x-ray attenuation information representing the container andan overlap region wherein the background object, the container and theunknown object of interest overlap.

Next, at step 2304, the dual-energy attenuation images are decomposedinto reference material equivalent path length images, which areprovided at step 2306. At step 2308, the reference material equivalentpath lengths representing the background object are removed from thereference material equivalent path length images. This may be done, forexample, using the methods described above with respect to backgroundobject removal. Thereby, there is provided at step 2310 referencematerial equivalent path lengths representing the unknown object and thecontainer.

At step 2312, the reference material equivalent path lengthsrepresenting the unknown object are converted to unknown object pathlengths multiplied by a predetermined scaling factor. Such a conversionmay be accomplished, for example by applying the following function foreach of the first and second reference material equivalent path lengthsrepresenting the unknown object:

${t_{o}\left( {i,j} \right)} = {\frac{\rho\;{t_{ob}\left( {i,j} \right)}}{\rho_{o}}\left\{ \frac{{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}}{{g\left\lbrack Z_{o} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right\}}$$\begin{matrix}{{t_{o}^{*}\left( {i,j} \right)} = {\rho\;{t_{ob}\left( {i,j} \right)}\left( {{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right) \times {scaling}\mspace{14mu}{factor}}} \\{= {{{t_{o}\left( {i,j} \right)} \times {scaling}\mspace{11mu}{factor}} = {{t_{o}\left( {i,j} \right)} \times {SF}}}}\end{matrix}$${{With}\mspace{14mu}{SF}} = {{\frac{1}{\rho_{o}\left( {{g\left\lbrack Z_{o} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right)}\mspace{14mu}{when}\mspace{14mu}{t_{o}^{*}\left( {i,j} \right)}} = {t_{o}\left( {i,j} \right)}}$wherein ρ_(o), g[Z_(o)] and g[Z_(b)] are all constants. Next, at step2314, the effective atomic number for each pixel representing theunknown object and the container is determined.

At step 2316, the mass thickness for each pixel representing the unknownobject and the container is determined. The mass thickness is equivalentto the unknown object path lengths representing the unknown object ofinterest multiplied by the scaling factor. At step 2318, there isidentified each first source-detector pair line defined by a first x-rayextending between a first one of the at least two sources and onedetector of the array of detectors in a first one of the plurality ofdual-energy attenuation images on which lies one scaled unknown objectpath length. At step 2320, there is identified each secondsource-detector pair line defined by a second x-ray extending between asecond one of the at least two sources and one detector of the array ofdetectors in a second one of the plurality of dual-energy attenuationimages on which lies one other scaled unknown object path length, thesecond one of the plurality of dual-energy attenuation images havingbeen generated contemporaneously with the first one of the plurality ofdual-energy attenuation images.

At step 2322, the extremities of each of the scaled unknown object pathlengths are joined to provide a scaled contour of the unknown object atstep 2324. The contour of the unknown object of each of the first andthe second one of the plurality of dual-energy attenuation images arethen iteratively matched at step 2326 to reduce the scaling factor ofthe scaled unknown object path lengths representing the unknown objectand provide unknown object path lengths at step 2328 and thereby acontour of the unknown object at step 2330.

The contour of the unknown object is then defined as an inner contour ofthe container at step 2332. At step 2334, there are identified thirdsource-detector pair lines defined by third x-rays extending betweeneach source and one detector of the array which intersect with thecontainer at only one point of intersection in each of the first andsecond one of the plurality of dual-energy attenuation images. Thesethird source-detector pair lines delimit at step 2336 an outer bound ofthe container as the pixels within the third source-detector pair lines.At step 2338, the outer bound of the container extending between the onepoint of intersection of each third source-detector pair line isinterpolated to define an outer contour of the container at step 2340.At step 2342, path lengths are determined which represent the containeras path lengths which extend between the inner contour of the containerand the outer contour of the container. Next, at step 2344, an effectiveatomic number of the unknown object is determined and at step 2346, amass density of the unknown object is determined.

Decomposition of the dual-energy attenuation images of the unknownobject at step 2304 into reference material equivalent path lengthimages may be performed in any manner previously described, such as forexample, imposing the dual-energy attenuation information of each pixelonto suitable inverse attenuation surfaces to obtain the first andsecond equivalent reference material path lengths as in step 2348 or byusing suitable lookup tables as in step 2350. This is previouslydiscussed with reference to FIGS. 3 and 11 and in particular step 306shown in FIG. 11.

The step 2306 for removal of reference material equivalent path lengthsrepresenting the background object, such as a security screening tray,from the images may be performed in a number of ways depending on theproperties of the background object.

The first method for removal of background objects, shown in FIG. 24, isto first, at step 2400, scan predetermined background objects, such as,for example, empty trays at various locations on the scanner belt and invarying angles of rotation or orientation within the scanning chamber toprovide low and high energy x-ray signal images at step 2402. The lowand high energy x-ray signal information for each pixel in each of thescans of the tray, along with position and angle data of the tray, arestored in a database at step 2404. This is done, for example, bycontouring the tray image and tracing a rectangle around it with asegmentation algorithm, as shown at step 2406, and saving the measuredvalues of the image and the corresponding tray placement information ina database. Then, when an unknown object of interest is scanned at step2408 in a tray using the x-ray scanner to provide low and high energyx-ray signal images of the unknown object overlapping with the tray atstep 2410, the stored tray image that is closest in position and angleto that scanned with the unknown object of interest is found in thedatabase at step 2412, once again, for example, by tracing a rectanglearound the tray using a segmentation algorithm at step 2414 and thencomparing at step 2416 that rectangle to the positions and angles of thetray in the stored database tray images. The database tray image is thenregistered at step 2418 on the scanned image of the unknown object ofinterest, simply by rotating and translating it so the angle andposition are a closer match. Finally, the tray image low and high energysignals are subtracted from the scan image at step 2420 to providebackground-free low and high energy signals representing only theunknown object at step 2422.

The second method for removal of background objects is very similar tothe first method, except that in addition to saving the empty traysignal data, the reference material path lengths, from the calibrationmethod, are also saved. Once again this is done by contouring the trayimage and preferably tracing a rectangle around it with a segmentationalgorithm and saving the measured values of the image as well as thecalculated reference material path lengths and the corresponding trayplacement and orientation information in a database. Then, when anunknown object of interest is scanned in a tray in the x-ray scanningdevice, the stored tray image that is closest in position andorientation is found in the database. This is preferably done as in thefirst method by tracing a rectangle around the tray of the scanned imageand then comparing that rectangle to the stored database tray images'positions and angles. The database tray image is then registered on theobject scanned image, preferably by rotating and translating it so theangle and position are a closer match. Then, during the next step,instead of subtracting the tray image signals from the scanned trayimage as in the first method, the reference materials path lengths ofthe tray image are subtracted from the reference materials path lengthsof the scanned image. This second method is therefore in accordance withthe method for removal of background object path lengths discussed abovewith reference to FIG. 14.

The third method for removal of background objects from a scanned imageis to directly apply the procedure explained previously relating to theremoval of a background object with homogeneous composition andnon-uniform path length distribution. With this method, the tray pathlengths in the region of overlap of the background object or tray andobject of interest must be known, as well as the density and effectiveatomic number of the material the tray is made of, in order to calculatethe mass thickness of the tray to be removed from the mass thickness ofthe scan image. They can be calculated by first obtaining or creating a3D model of the tray. Then the position and rotation angle of the trayin the scanner must be determined. This can be done once again using asegmentation algorithm and preferably by tracing a rectangle around thetray in the scan image. The 3D model of the tray is then simulated inthe scanner geometry with the proper position and angle. A ray castingalgorithm may be used to find the path lengths through the tray forevery pixel. The ray casting algorithm can be executed by the graphicsprocessing unit (GPU) to speed up the process. If they have not beendetermined beforehand, the tray density and effective atomic number canbe obtained from the image by applying the dual-reference material pathlength decomposition method previously described. With both thesematerial properties and the tray path lengths, it is possible tocalculate the reference material path lengths for the whole tray. Thesereference material path lengths can then be subtracted from thereference material path lengths of the overlap region of the image,which results in the reference material path lengths of the imagewithout the tray. These reference material path lengths can then be usedto calculate the signal, attenuation, mass density and effective atomicnumber for the image without the tray.

With reference to FIG. 25, the third method for removal of backgroundobjects begins with the step 2500 of scanning a predetermined backgroundobject to provide low and high energy x-ray signal images at step 2502.At step 2504 there is obtained a three-dimensional model of thebackground object according to the position and orientation of thebackground object as scanned in the x-ray scanning device. At step 2506,the reference material equivalent path lengths through the backgroundobject in the three-dimensional model are determined for each pixelusing a ray casting algorithm as shown at step 2508 or any othersuitable reference material decomposition means as previously described.The effective atomic number of each pixel the background object isdetermined at step 2510 and the mass density of each pixel of thebackground object is determined at step 2512. Next, at step 2514, themass thickness of the background object is determined by multiplying thepredetermined first and second reference material equivalent pathlengths of the background object with the mass density of the backgroundobject. At step 2516, the background object and overlap region arelocalized in the dual-reference material equivalent path length imagesof the unknown object scanned with the background object, preferablyusing a segmentation algorithm as shown at step 2518. At step 2520, themass thickness of the background object is eliminated from the massthickness of the reference material path length images to obtain a massthickness of the unknown object at step 2522. The first and secondreference material equivalent path lengths through the unknown objectare thereby provided at step 2524.

A preferred next step in the method described in FIGS. 23A and 23B is todetermine the effective atomic number (Z_(eff)) of the container asshown at step 2352, if the container is present. The calibration methoddescribed above transforms the signal obtained for each pixel of thescanned image into mass thickness and Z_(eff) values. If the X-raycorresponding to a pixel has traversed multiple different materials, theresulting mass thickness and Z_(eff) are combinations (sum and weightedaverage) of the properties of those materials. In order to find theeffective atomic number of the container, a pixel of an X-ray thattraverses the container but not the object of interest must be observed.This can happen two possible ways: observation of a pixel representingthe “side” of the container in the scanned image, and, observation of apixel representing the “top” (whichever side is up) of the container,where there is no object of interest at that portion of the containerbecause of gravity. In these locations, the Z_(eff) of the container canbe directly obtained from the calibration method. The Z_(eff) valuesassociated with each pixel may be found, for example, by applying asegmentation procedure to the scan image, and then calculating theaverage (or another relevant statistical quantity) effective atomicnumber over the region of the container. If there is no container, ormore specifically the object of interest is not contained within acontainer, the mass thickness of each pixel, obtained from the abovedescribed calibration method, is equivalent to the object of interestdensity multiplied by the object of interest path length for that pixel.In that case, the density, which is unknown but constant across allpixels, acts as a scaling factor. Therefore, the mass thickness is ascaled version of the path lengths. If there is a container, then theprocedure explained above with reference to FIGS. 17A and 17B inrelation to the removal of a background object with a homogenouscomposition and non-uniform path length distribution may be used toevaluate the mass thickness of a material in the calibration method ifthe mass thickness and effective atomic number from the combination ofboth materials, as well as both of the materials' individual effectiveatomic numbers are known. This is true for the reference materials ofthe calibration method, but is also true for the container and object ofinterest materials:

${\rho_{o}{t_{o}\left( {i,j} \right)}} = {\rho\;{t_{ob}\left( {i,j} \right)}\left\{ \frac{{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}}{{g\left\lbrack Z_{o} \right\rbrack} - {g\left\lbrack Z_{b} \right\rbrack}} \right\}}$${\rho_{b}{t_{b}\left( {i,j} \right)}} = {\rho\;{t_{ob}\left( {i,j} \right)}\left\{ \frac{{g\left\lbrack {Z_{ob}\left( {i,j} \right)} \right\rbrack} - {g\left\lbrack Z_{o} \right\rbrack}}{{g\left\lbrack Z_{b} \right\rbrack} - {g\left\lbrack Z_{o} \right\rbrack}} \right\}}$where (i,j) is the pixel coordinates in the image, pt is the massthickness, g(Z) the effective atomic number model, the indices “o”stands for “object of interest”, “b” for background or bottle(container), “ob” for object of interest+background. ρt_(ob)(p) andg[Z_(ob)(i, j)] are obtained directly from the above describedcalibration method and g[Z_(b)] was obtained during the last step.

However, since the Z_(eff) and mass thickness are a combination of theunderlying materials and because of the nature of the objects beingscanned (object of interest within a container), there are no pixelsrepresenting only the object of interest. Also, there is no way ofapplying the layer removal procedure to the container without eitherhaving either the exact 3D model of the container or some pixels withonly container information and knowledge of the path length of thex-rays through the container in those pixels. Neither of these pieces ofinformation are available and g[Z_(o)] remains unknown. Therefore, themass thickness of the object of interest or container cannot beevaluated directly. However, values for the path lengths through theobject of interest multiplied by a constant, called a scaling factor,may still be determined from the previous equations, by estimating valuefor g[Z₀]. The result is a value that represents the path lengthsmultiplied by a constant, called scaling factor. Although the scalingfactor is unknown, it is the same for all pixels, which is sufficientfor this step of the procedure. Also, as explained previously, inparticular with respect to the aforementioned procedure for removal of abackground object having homogenous composition and horizontally uniformpath length distribution, the uncertainties for all formulations ((t1,t2) or (ρt, Z)) of the input values are known. It is therefore possibleto evaluate uncertainty, on the object of interest path lengthsdetermined with the present method. This information may be used toaffect the results in the subsequent steps.

Mass thickness is already equivalent to the path lengths multiplied byan unknown constant (the density). As it was explained previously,multiplying the path lengths by an arbitrary constant, still results inthe path lengths multiplied by an unknown constant called the scalingfactor. This step is about transforming a set of separate path lengthsinto a cohesive object of interest shape and eliminating the scalingfactor to find the real path lengths.

For a given scaling factor, the initial data set is composed of pathlengths for each pixel, for all images generated by each source, or inother words the length of the intersection for each X-ray and the objectof interest. Each detector-source pair is represented as a known linethrough space on which the corresponding path length through the objectof interest is located. Since the exact shape and location of the objectof interest is unknown, the position of the path length line segmentalong its supporting line is also unknown. However, all source-detectorsassemblies view the same object. Therefore, the contour of the object ofinterest in a given slice, created by joining the extremities of eachpath length with the extremities of its nearest neighbors, should be thesame in both views. Moving a path length along its supporting linemodifies the object of interest contour in two points, since its linemust both “enter” and “exit” the object of interest. The goal of thisstep is to move the path lengths so that the contours formed from everyview's path lengths are as similar as possible. Such movement may beaccording to pre-specified rules and constraints. Thereby, the contoursmay be superimposed in space and iteratively moved towards each other,since, if the contours found in two contemporaneous images generated bytwo different sources circumscribe the same space, then it means thatthe two contours are very similar. However, if the path lengths are toolong, it may be difficult to obtain such a result.

This process is similar to non-rigid point set registration, but wherethe different sets of points are being registered on each other, so allsets of points act as both the “source” and “target” at the same time.Accordingly, the conventional registration metrics are generalized totake that into account. Therefore, it can be divided into two mainsteps.

First, the distance between the sets of data representing the contour inboth images is measured in some way. This may be done either for eachpoint in each set (with particular attention spent on the fact that theamount for each set is different) or for the set as a whole or both.

Second, the points of each set are displaced to reduce the distancemeasured in the previous step. The points in each set can be displacedindividually, as a whole or both. However, contrary to regularregistration procedures, the points can only be moved parallel on theirsupporting lines, which means the displacement cannot only be acombination of translation and rotation of the whole set of points.Therefore, the points must be at least displaced individually.

The above two steps may be repeated until the desired level of “match”is attained. This can be defined either by a threshold on the distancemeasured in step one or the displacement of step two. The procedure canalso be stopped after a certain number of iterations has been reached.

This procedure can be repeated separately for each column in the image,also called a “slice”. A slice is the corresponding columns in the imageof each view acquired at the same time from the beginning of the scan ofthe object. Since the different sources irradiated parallel planes andthe belt moves at constant speed, the length of the container in everyimage is the same. The subdivision of the container lengthwisecorresponds to the pixel columns in the image, and is determined by thebelt speed and integration time of the electronic acquisition system,which is the same for both views. Therefore, each column in one viewcorresponds to another column in the other view that sees the samesection of the container, or the same “slice”, up to the spatialresolution of the detection system.

However, it is possible that this first scaling factor may not becorrect or optimal. The contour matching procedure is started at thelargest possible scaling factor then repeated for increasingly smallerscaling factors. This repetition is stopped when the contours attain thebest “level of match” compared to other scaling factors. By iterativelychoosing a scaling factor that is closer to the correct one, the “levelof match” should increase. When the “level of match” starts decreasing,this means that the scaling factor is moving further from the correctvalue, which makes it possible to evaluate the correct scaling factor.This procedure may be performed for several slices together orseparately.

In a next step, the container is reconstructed which in turn includesthe determination of the bounding box of the container and a bubble, ifpresent.

A bounding box is a set of lines that limits the area where the pathlengths must be contained and is defined by the edge pixels from allviews. The container bounding box is made of lines intersecting eachother. Since these lines are considered continuous in space, they do notinitially limit the permitted space to a polygon, as they should. Forthe object of interest, this is avoided by defining the bounding pointsfor each source-detector supporting line supporting each scaled pathlength, and the points defining the object of interest must be inbetween those bounding points. This procedure does not provide asuitable bounding box for the container, since the container points thatwill be created will not be necessarily be on the supporting lines.Therefore, the actual bounding polygon for the container must bedefined. This is done by finding all the bounding lines intersectionsand eliminating all points that are too far from the previouslymentioned bounding points. The bounding polygon is then simply the linejoining together all the points left. Also, when three bounding linesintersect at the same point, they usually appear as three intersections.In that case, the middle intersection is eliminated from the polygon.This creates a very small segment instead of a 3-way intersection point.This very small segment will be useful in further steps.

In a next step, the presence of an empty part inside the container, alsocalled a bubble, is detected when present, either by comparing theestimated thickness of the container under and above the container or byother means. The points composing the top surface of the object ofinterest are also determined.

The container path lengths are determined differently than the pathlengths for the object of interest. First, a model or contour must becreated for the container, which is done by “anisotropic scaling” of theobject of interest, so it touches the container bounding box. There areas many contact points of the scaled object of interest contour as thereare bounding box polygon sides. This can be done by applying fivehypotheses that can be relatively safely assumed about the container, inaddition to the previous rules and constraints that were used for theobject of interest reconstruction. First, for any path length that doesnot extend into an empty part of the container, the object of interestinside touches the container at both entry and exit points of object ofinterest path lengths. Second, the container must touch each side of thecontainer bounding box in at least one location. Third, although thecontainer thickness will generally not be constant, it should be asmooth function in between points of contact with the bounding box. Thiscan be achieved by interpolating the thickness between points ofcontact. Fourth, the point of contact on the bounding box is likely tobe either the one closest to the object of interest, or the one that isencountered when travelling along the normal of the object of interesttop surface. Fifth, if a bubble was detected and the part of the objectof interest that was closest to the bounding box is part of the topsurface of the object of interest, this side of the bounding box shouldnot be considered, since the exact point where the container is incontact with the bounding box is difficult to determine based on theobject of interest.

The first hypothesis allows for the creation of the inner contour of thecontainer, which is simply equal to the contour of the object ofinterest. The four subsequent hypotheses allow the creation of the outercontour of the container. To create a contour, whether inner or outer,corresponding model points are linked in the same order as the object ofinterest contour points. Container path lengths are then obtained byintersecting the supporting lines with that shape using, for example, aray casting algorithm. If the intersection would be outside the boundingbox, the intersection with the bounding box is used instead for thatpath length. Finally, the container contour is created by joining theextremities of these path lengths, as for the object of interestcontour.

If the container is too thin, the bounding box of the liquid (object ofinterest) may be the same as the bounding box of the container. In thatcase, the “anisotropic scaling” method is not optimal. The preferredalternative is to suppose instead that the container thickness isconstant. This thickness may be a preset constant, may be inferred fromthe geometrical transverse distance between adjacent pixels, or may beestimated from the Zeff of the container or by other means.

If a bubble is present in the container, then the container model may beerroneous, and a different model would be preferred. One such model useseither reflection or rotational symmetry to create the container,depending on the previously determined number of corners. Indeed,containers with an even number of corners (and sides) are more likely tohave vertical symmetry, whereas it is impossible for a container with anodd number of corners/sides to possess “vertical” symmetry if it has aside lying flat on the tray surface. Note here that vertical refers tothe axis that is normal to the tray surface on which the container islying.

Reflection symmetry can be useful if the top part of the container ispoorly defined but the bottom part is well defined, and the container issuspected to be vertically symmetrical. In such circumstances, anadditional procedure is used to modify the container model whichdifferentiates points that are part of the object of interest/bubbleinterface and points that are part of the object of interest/containerinterface. The latter, as well as the container points, are reflectedbased on an axis that is parallel to the tray surface. The reflectedcontainer points must also be tangential to the bounding box. Finally,points left under the reflection axis are eliminated, and sections ofcontour missing are interpolated.

Another way to determine the thickness of the container all around theobject of interest contour, is to first evaluate the thickness accordingto the previously detailed model. Then the periodicity of the containerthickness and/or object of interest radial size is evaluated. If it isdetermined to have a clear period, then the thickness can be taken fromone period and then repeated for the other periods.

This can be particularly useful if there are few contact points and thereal container thickness shifts in a way that is nonlinear in betweenthose points. In that case it is possible that the container contourunder the object of interest is more accurately defined because of theproximity with the bounding box. This case can be detected if the normalcontainer model leads to a container thickness over the object ofinterest that is much larger than the one underneath it.

In that case, the periodicity of the object of interest or containershape may be evaluated, either by performing a fast Fourier transform onthe radial size of the object of interest or by other means. If theshape is found to be periodic or if a bubble has been detected, then aspreviously indicated, the period is evaluated and the container contours(both inner and outer) are taken over a period and repeatedly rotatedaround the most likely centroid of the container to form a completecontour. The most likely segment of contour to be estimated correctly isthe one located directly under the container centroid, between thebounding box surface and the liquid.

Solution by pairs provides a second method of determining the thicknessof the container around the object of interest. The solution by pairscorresponds to solving the two base equations (individually):ρt _(ob)(i,j,k)=ρ_(o) t _(o)(i,j,k)+ρ_(b) t _(b)(i,j,k)g[Z _(ob)(i,j,k)]ρt _(ob)(i,j,k)=g[Z _(o)]ρ_(o) t _(o)(i,j,k)+g[Z_(b)]ρ_(b) t _(b)(i,j,k)for pairs of path lengths, transforming a situation of 2 equations-3unknowns for a single path length, to 4 equations-3 unknowns.

All possible pairs of pixels i can be used, as long as its supportingline sees both the object of interest and the container, even if theybelong to different slices j and views k. Pairs of resulting values thatare outside the range of possible values can be eliminated outright, andare most likely caused by an incorrect path length. Each pair will givea different value for ρ_(o), ρ_(b) and Z_(o), and so this method resultsin a distribution of values. The best value for each quantity isevaluated from descriptive statistics of the associated distribution. Itcan be also relatively safely assumed that the lower the spread of thedistribution, the more optimal the solution is likely to be.

There is provided a third method for determining the thickness of thecontainer wall whereby analytical functions may be fit on the data. Thismay be done in two different ways, for both of the base equationsreferred to in the above description for the solution by pairs. All fitsare made using quantities for all pixels i, slices j and views k.

The first fitting option is a linear fit on the following equations:

$\frac{\rho\;{t_{ob}\left( {i,j,k} \right)}}{t_{b}} = {{\rho_{o}\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}} + \rho_{b}}$with the regressor

$\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}$and the predictor

${\frac{\rho\;{t_{o}\left( {i,j,k} \right)}}{t_{b}}\frac{{g\left\lbrack {Z_{ob}\left( {i,j,k} \right)} \right\rbrack}\rho\;{t_{ob}\left( {i,j,k} \right)}}{t_{b}\left( {i,j,k} \right)}} = {{{g\left\lbrack Z_{o} \right\rbrack}\rho_{o}\frac{t_{o}\left( {i,j,k} \right)}{t_{b}\left( {i,j,k} \right)}} + {{g\left\lbrack Z_{b} \right\rbrack}\rho_{b}}}$

with the regressor

$\frac{t_{o}\left( {i,j,k} \right)}{t_{b}}$and the predictor

$\frac{{g\left\lbrack {Z_{ob}\left( {i,j,k} \right)} \right\rbrack}\rho\;{t_{ob}\left( {i,j,k} \right)}}{t_{b}\left( {i,j,k} \right)}$By fitting a linear regression, the slope of the first equation is ρ_(o)and the slope of the second equation is g[Z_(o)]ρ_(o). The intersect inthe first equation gives ρ_(b). Note that for both equations, o and bcan be switched interchangeably to instead find the container density asthe slope and object of interest density as the intersection. However,this has limited use since at this point the properties of the object ofinterest may be calculated without having to find the container density.

The second fitting option is to consider the base equations as bivariatelinear functions:ρt _(ob)(i,j,k)=ρ_(o) t _(o)(i,j,k)+ρ_(b) t _(b)(i,j,k)with the regressors t_(o) (i,j,k) and t_(b) (i,j,k), and the predictorρt_(ob)(i,j,k)g[Z _(ob)(i,j,k)]ρt _(ob)(i,j,k)=g[Z _(o)]ρ_(o) t _(o)(i,j,k)+g[Z_(b)]ρ_(b) t _(b)(i,j,k)

with the regressors t_(o) (i,j,k) and t_(b) (i,j,k),

-   -   and the predictor g[Z_(ob)(i,j,k)]ρt_(ob)(i,j,k)        For the first equation, the slope in direction x at y=0 is ρ_(o)        and the slope in direction y at x=0 is ρ_(b). For the second        equation, the slope in direction x at y=0 is g[Z_(o)]ρ_(o) and        the slope in direction y at x=0 is g[Z_(b)]ρ_(b).

Finally, g[Z_(o)] can be obtained by dividing g[Z_(o)]ρ_(o) by thepreviously obtained ρ_(o), and Z_(o) can be obtained with g⁻¹{g[Z_(o)]}.

It should be understood that the object of interest may not necessarilybe contained within a container. Under such circumstances, the methodmay proceed as follows with a number of steps being similar or identicalto those found within the method wherein the object of interest iscontained within a container, however, wherein determination of thecontainer characteristics and bounding box is not required.

With reference to FIG. 26, the method for assigning attributes to anobject of interest in another aspect may be described as follows.However, it should be understood that certain steps in the method may beperformed by different means, depending on the conditions relating tothe object of interest that is scanned without departing from the scopeof the invention described herein. Certain steps may also be performedin a different order than that presented in the following description.

In a first step 2600, the unknown object of interest is scanned.Typically, the object of interest at least partially overlaps with abackground object within an x-ray scanning device, such as, for example,a security screening tray. The x-ray scanning device emits x-rays fromat least two sources which pass through the unknown object and thebackground object to be detected by at least one array of detectors. Thedetectors provide at step 2602 a plurality of dual-energy attenuationimages each having dual-energy x-ray attenuation informationrepresenting an overlap region wherein the background object and theunknown object of interest overlap.

Next, at step 2604, the dual-energy attenuation images are decomposedinto reference material equivalent path length images, which areprovided at step 2606. At step 2608, the reference material equivalentpath lengths representing the background object are removed from thereference material equivalent path length images. This may be done, forexample, using any of the methods described above with respect tobackground object removal. Thereby, there is provided at step 2610reference material equivalent path lengths representing the unknownobject.

At step 2612, the reference material equivalent path lengthsrepresenting the unknown object are converted to unknown object pathlengths multiplied by a predetermined scaling factor.

At step 2614, the mass thickness for each pixel representing the unknownobject is determined. The mass thickness is equivalent to the unknownobject path lengths representing the unknown object of interestmultiplied by the scaling factor. At step 2616, there is identified eachfirst source-detector pair line defined by a first x-ray extendingbetween a first one of the at least two sources and one detector of thearray of detectors in a first one of the plurality of dual-energyattenuation images on which lies one scaled unknown object path length.At step 2618, there is identified each second source-detector pair linedefined by a second x-ray extending between a second one of the at leasttwo sources and one detector of the array of detectors in a second oneof the plurality of dual-energy attenuation images on which lies oneother scaled unknown object path length, the second one of the pluralityof dual-energy attenuation images having been generatedcontemporaneously with the first one of the plurality of dual-energyattenuation images.

At step 2620, the extremities of each of the scaled unknown object pathlengths are joined to provide a scaled contour of the unknown object atstep 2622. The contour of the unknown object of each of the first andthe second one of the plurality of dual-energy attenuation images arethen iteratively matched at step 2624 to reduce the scaling factor ofthe scaled unknown object path lengths representing the unknown objectand provide unknown object path lengths at step 2626 and thereby acontour of the unknown object at step 2628. Next, at step 2630, aneffective atomic number of the unknown object is determined and at step2632, a mass density of the unknown object is determined.

Decomposition of the dual-energy attenuation images of the unknownobject at step 2604 into reference material equivalent path lengthimages may be performed in any manner previously described, such as forexample, imposing the dual-energy attenuation information of each pixelonto suitable inverse attenuation surfaces to obtain the first andsecond equivalent reference material path lengths as in step 2634 or byusing suitable lookup tables as in step 2636. This is previouslydiscussed with reference to FIGS. 3 and 11 and in particular step 306shown in FIG. 11.

Since multiple values have been obtained for the object of interestproperties, the values must be combined to provide a final best valueaccording to a set of criteria based on various evaluable metrics. Thedisparity, uncertainties of the values as well as the uncertainty on thescaling factor determined in relation to the contour of the object ofinterest, and various metrics determined by these can all be consideredin determining the final values, as well as their uncertainties. Theseuncertainties may be relied upon in the next step, the threatdetermination method.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

Threat Determination Method

The purpose of the threat determination method is to calculate a threatmetric value and a safe metric value by comparing the Z_(eff) anddensity ranges of the object of interest, determined by way of themethods defined previously, to threat and safe maps built by scanningactual explosives and safe objects. A decision is made based on thesevalues and if a threat is detected, it is shown on screen for viewing bysecurity screening personnel or an alert condition is raised.

The density and Z_(eff) values of objects considered to be threats andsafe are used to build the maps. These can be acquired either by lookingin literature, making measurements, calculating properties from thechemical composition, using the calibration method presented above orusing scans and the method for object reconstruction described above, ora combination of these methods. The density/effective atomic numberjoint distribution depends on the source of the value or the method usedfor its acquisition. Then for each point of the whole domain of possibleobject density and Z_(eff) values (wherein the distribution is such thatdensity is on one axis and Z_(eff) is on the other axis), theprobability density of each known object of the corresponding map issuperimposed. So, for the pair (density, Z_(eff)), the probability forOBJECT 1 to have one specific (density, Zeff) is added to the map, theprobability of OBJECT 2 to have one specific (density, Zeff) is added tothe map, etc., until all objects for that category (safe or threat) havebeen added to the map. This is done for all possible (density, Z_(eff))pairs of the density and Z_(eff) domain. Each map is then normalized forthe number of objects it contains. The map therefore returns, for aspecific (density, Zeff) pair, both “threat” and “safe” values that aresimilar to a probability, that each represent how likely it is for thatpair to be a threat and a safe object.

Note that this step can be performed by using a suitable density/Z_(eff)mesh and by calculating the safe and threat metrics for each cell of themesh, or analytically by considering the sum of probabilities densitiesfor each object as continuous functions over the domain. An example of aprobability density for an object could be a binormal distributioncentered on the average density and Z_(eff) of that object. Thenormalized sum of all the distributions of the objects of one category,“safe” of “threat” are respectively called the safe map and threat map.

When an unknown object is scanned, a similar distribution is determinedfor that object as a result of the object reconstruction method,described above. This is called the value distribution.

The threat and safe metrics are simply the sum of the value distribution(assumed once again as a normal distribution) multiplied by eachcorresponding map, over the whole map:

$\mspace{76mu}{{{Safe}\mspace{14mu}{metric}} = {\sum\limits_{i}{{safe}\mspace{14mu}{{map}\left( {\rho_{i},Z_{{eff},i}} \right)}*{value}\mspace{14mu}{{distribution}\left( {\rho_{i},Z_{{eff},i}} \right)}}}}$${{Threat}\mspace{14mu}{metric}} = {\sum\limits_{i}{{threat}\mspace{14mu}{{map}\left( {\rho_{i},Z_{{eff},i}} \right)}*{value}\mspace{14mu}{{distribution}\left( {\rho_{i},Z_{{eff},i}} \right)}}}$Here, the index i refers to each cell of the map, and ρ_(i),Z_(eff,i)represent the mass density and Z_(eff) for each of those cells.

For example, for the first cell, the safe metric value will be the“safe” value previously defined for the mass density and Z_(eff) of thatfirst cell, multiplied by the probability that the unknown object hasthat mass density and Z_(eff). This is repeated for each cell, and theresults are added together to provide the safe metric. This is done onceagain but with the threat map to provide the threat metric.

Or, if the maps are analytical,

$\;{{{Safe}\mspace{14mu}{metric}} = {\underset{- \infty}{\overset{\infty}{\int\int}}{safe}\mspace{14mu}{{map}\left( {\rho,Z_{eff}} \right)}*{value}\mspace{14mu}{{distribution}\left( {\rho,Z_{eff}} \right)}d\;\rho\;{dZ}_{eff}}}$${{Threat}\mspace{14mu}{metric}} = {\underset{- \infty}{\overset{\infty}{\int\int}}{threat}\mspace{14mu}{{map}\left( {\rho,Z_{eff}} \right)}*{value}\mspace{14mu}{{distribution}\left( {\rho,Z_{eff}} \right)}d\;\rho\;{dZ}_{ef}}$

If the unknown object of interest has been determined to have propertiesthat are similar to a region of the map with a higher concentration ofpossible safe/threat mapped objects, then it will appropriately havecorresponding higher safe/threat metrics.

The threat metric is divided by or otherwise mathematically combinedwith the safe metric to give the threat ratio, and if the threat ratiois over the decision threshold, then the unknown object is a threat. Thethreshold is selected to maximize detection and minimize falsepositives, and its concept is thoroughly studied in decision theory. Itcan also be experimentally determined by scanning objects in differentconfigurations, conditions, containers, and evaluating the resultingsafe and threat metrics. The adjustment of the threshold then results ina number of safe and threat assessments, therefore resulting in aproportion of false positives and detection rates. It is then fixed toresult in the optimal proportion for the decision objectives dictated byexternal authorities and is dependent on the overall solution.

If the unknown objects or objects of interest are determined to bethreats, the pixels they occupy in the images are sent to the GUI partof the software for highlighting and user warning. An alert conditionmay also be raised.

With reference to FIG. 27, there is provided a method for assigning oneof a safe condition and a threat condition to an unknown object. Themethod begins with the step 2700 of determining a density value and aneffective atomic number value for a plurality of predetermined safeobjects and a plurality of predetermined threat objects. At step 2702,the density value and effective atomic number values of each of thepredetermined safe objects and predetermined threat objects are plottedin a probability map to correlate corresponding pairs of density valuesand effective atomic number values with each of the predetermined safeobjects and predetermined threat objects.

At step 2704 an unknown object is scanned to provide a plurality ofdual-energy attenuation images at step 2706 each having dual-energyattenuation information representing the unknown object. At step 2708,each of the dual-energy attenuation images are decomposed intodual-reference material equivalent path length images representing theunknown object, provided at step 2710. The reference material equivalentpath lengths representing the unknown object are converted at step 2712into unknown object path lengths multiplied by a predetermined scalingfactor.

At step 2714, the effective atomic number for each pixel representingthe unknown object is determined. At step 2716, the effective atomicnumber of the unknown object is imposed on the probability map todetermine a probability that the unknown object is correlated with oneof a predetermined safe object or a predetermined threat object,provided at step 2718. As a further optional step, an alert may beraised at step 2720 based on this probability. Such an alert may, bynon-exhaustive example, be an audible alert, a modification to thedisplayed image, or notification to the appropriate personnel, amongother suitable alert conditions.

Decomposition of the dual-energy attenuation images of the unknownobject at step 2710 into reference material equivalent path lengthimages may be performed in any manner previously described, such as forexample, imposing the dual-energy attenuation information of each pixelonto suitable inverse attenuation surfaces to obtain the first andsecond equivalent reference material path lengths as in step 2722 or byusing suitable lookup tables as in step 2724. This is previouslydiscussed with reference to FIGS. 3 and 11 and in particular step 306shown in FIG. 11.

Moreover, in cases wherein removal of a background object orreconstruction of an object may be required, such removal of thebackground object and/or reconstruction may be performed accordingly toany suitable method previously described.

A system of one or more computers can be configured to perform theparticular operations or actions as described herein by virtue of havingsoftware, firmware, hardware, or a combination of them installed on thesystem that in operation causes or cause the system to perform theactions automatically and in real time or near real time. One or morecomputer programs can be configured to perform particular operations oractions described herein by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions. Such actions may be performed automatically and in realtime or near real time.

While the invention has been described in terms of specific embodiments,it is apparent that other forms could be adopted by one skilled in theart. For example, the methods described herein could be performed in amanner which differs from the embodiments described herein. The steps ofeach method could be performed using similar steps or steps producingthe same result but which are not necessarily equivalent to the stepsdescribed herein. Some steps may also be performed in different order toobtain the same result. Similarly, the apparatuses and systems describedherein could differ in appearance and construction from the embodimentsdescribed herein, the functions of each component of the apparatus couldbe performed by components of different construction but capable of asimilar though not necessarily equivalent function, and appropriatematerials could be substituted for those noted. Accordingly, it shouldbe understood that the invention is not limited to the specificembodiments described herein. It should also be understood that thephraseology and terminology employed above are for the purpose ofdisclosing the illustrated embodiments, and do not necessarily serve aslimitations to the scope of the invention.

What is claimed is:
 1. A method for assigning an attribute to x-rayattenuation comprising: acquiring first and second reference materialequivalent path length information associated with a first range ofdual-energy x-ray attenuation information; acquiring second and thirdreference material equivalent path length information associated with asecond range of dual-energy x-ray attenuation information; and, joiningthe first dual-energy x-ray attenuation information range with thesecond dual-energy x-ray attenuation information range usingcoefficients representing dual-energy x-ray attenuation information ofthe second reference material to define a third dual-energy x-rayattenuation information range upon which may be imposed dual-energyx-ray attenuation values within the third dual-energy x-ray attenuationinformation range to determine corresponding first reference materialequivalent path lengths and third reference material equivalent pathlengths.
 2. The method as in claim 1, wherein the step of acquiringfirst and second reference material equivalent path length informationassociated with a first range of dual-energy x-ray attenuationinformation further comprises the steps of: scanning in an x-rayscanning device first and second reference materials each having knownatomic composition, known dimensions and known orientation in the x-rayscanning device, the x-ray scanning device emitting x-rays which passthrough the first reference material with first reference material pathlengths and through the second reference material with second referencematerial path lengths, the x-rays being detected by an array ofdetectors to provide first dual-energy x-ray attenuation information foreach of the first and second reference materials; associating the firstdual-energy x-ray attenuation information with each of the firstreference material path lengths and the second reference material pathlengths; and, expressing collectively each of the first referencematerial path lengths and the second reference material path lengths asa function of the associated first dual-energy x-ray attenuationinformation to define first dual-energy attenuation surfaces.
 3. Themethod as in claim 1, wherein the step of acquiring first and secondreference material equivalent path length information associated with afirst range of dual-energy x-ray attenuation information furthercomprises the steps of: retrieving from lookup tables saved first andsecond reference material equivalent path lengths associated with thedual-energy x-ray attenuation information corresponding with the firstdual-energy attenuation information range.
 4. The method as in claim 1,wherein the step of acquiring second and third reference materialequivalent path length information associated with a first range ofdual-energy x-ray attenuation information further comprises the stepsof: scanning in the x-ray scanning device the second reference materialand a reference third material having known atomic composition, knowndimensions and known orientation in the x-ray scanning device to providesecond low-energy x-ray attenuation information and high-energy x-rayattenuation information for each of the second and third referencematerials; associating each of the second low-energy x-ray attenuationinformation and the second high-energy x-ray attenuation informationwith each of the second reference material path lengths and thirdreference material path lengths; and, expressing collectively each ofthe second reference material path lengths and the third referencematerial path lengths as a function of the associated low-energy x-rayattenuation information and high-energy x-ray attenuation information todefine second high-energy attenuation surfaces and second low-energyattenuation surfaces.
 5. The method as in claim 1, wherein the step ofacquiring second and third reference material equivalent path lengthinformation associated with a second range of dual-energy x-rayattenuation information further comprises the steps of: retrieving fromlookup tables saved second and third reference material equivalent pathlengths associated with the dual-energy x-ray attenuation informationcorresponding with the second dual-energy attenuation information range.6. The method according to claim 2, wherein the step of expressingcollectively each of the first reference material path lengths and thesecond reference material path lengths further comprises the step of:selecting a model for expressing collectively each of the firstreference material path lengths and the second reference material pathlengths as a function of the associated first dual-energy x-rayattenuation information to define the dual-energy attenuation surfaces.7. The method according to claim 2, wherein the step of expressingcollectively each of the first reference material path lengths and thesecond reference material path lengths further comprises the step of:determining numerically pointwise inverted first dual-energy attenuationsurfaces using an optimization algorithm inverting the first dual-energyattenuation surfaces.
 8. The method according to claim 4, wherein thestep of expressing collectively each of the second reference materialpath lengths and the third reference material path lengths furthercomprises the step of: selecting a model for expressing collectivelyeach of the second reference material path lengths and the thirdreference material path lengths as a function of the associated seconddual-energy x-ray attenuation information to define the seconddual-energy attenuation surfaces.
 9. The method according to claim 4,wherein the step of expressing collectively each of the second referencematerial path lengths and the third reference material path lengthsfurther comprises the step of: determining numerically pointwiseinverted second dual-energy attenuation surfaces using an optimizationalgorithm inverting the second dual-energy attenuation surfaces.
 10. Themethod according to claim 6, wherein the model is a second model, thefirst dual-energy attenuation surfaces are first dual-energy inverseattenuation surfaces, respectively, and prior to the associating step,the method further comprising the steps of: associating each of thefirst dual-energy x-ray attenuation information with corresponding onesof each of the first material path lengths and the second material pathlengths; and, selecting a first model for expressing collectively thefirst dual-energy x-ray attenuation information as a function of thefirst reference material path lengths and the second reference materialpath lengths to define first direct attenuation surfaces.
 11. The methodaccording to claim 6, wherein the step of selecting the model furtherincludes the steps of: selecting a set of coefficients to be applied tothe model for fitting the first dual-energy x-ray attenuationinformation with the model; and, fitting the first dual-energy x-rayattenuation information with the model optimizing the coefficients. 12.The method according to claim 11, wherein the step of selecting themodel further includes the steps of: selecting the set of fittingconstraints to be applied to the model for selecting the coefficients;and, selecting the set of coefficients by applying the set of fittingconstraints to the model.
 13. The method according to claim 10, whereinthe step of selecting the first model further includes the steps of:selecting a first set of coefficients to be applied to the first modelfor fitting the first dual-energy x-ray attenuation information with thefirst model; and, fitting the first dual-energy x-ray attenuationinformation with the first model optimizing the first coefficients; and,the step of selecting the second model further includes the steps of:selecting a second set of coefficients to be applied to the second modelfor fitting the first dual-energy x-ray attenuation information with thesecond model; and, fitting the first dual-energy x-ray attenuationinformation with the second model optimizing the second set ofcoefficients.
 14. The method according to claim 13, wherein the step ofselecting the first model further includes the steps of: selecting afirst set of fitting constraints to be applied to the first model forselecting the first set of coefficients; and, selecting the set of firstcoefficients by applying the first set of fitting constraints to thefirst model; and, the step of selecting second the model furtherincludes the steps of: selecting a second set of fitting constraints tobe applied to the second model for selecting the second set ofcoefficients; and, selecting the second set of coefficients by applyingthe second set of fitting constraints to the second model.
 15. Themethod according to claim 6, wherein the model is a second model, thesecond dual-energy attenuation surfaces are second dual-energy inverseattenuation surfaces, respectively, and prior to the associating step,the method further comprising the steps of: associating each of thesecond dual-energy x-ray attenuation information with corresponding onesof each of the second material path lengths and the third material pathlengths; and, selecting a first model for expressing collectively thesecond dual-energy x-ray attenuation information as a function of thesecond reference material path lengths and the third reference materialpath lengths to define second direct attenuation surfaces.
 16. Themethod according to claim 8, wherein the step of selecting the modelfurther includes the steps of: selecting a set of coefficients to beapplied to the model for fitting the second dual-energy x-rayattenuation information with the model; and, fitting the seconddual-energy x-ray attenuation information with the model optimizing thecoefficients.
 17. The method according to claim 16, wherein the step ofselecting the model further includes the steps of: selecting the set offitting constraints to be applied to the model for selecting thecoefficients; and, selecting the set of coefficients by applying the setof fitting constraints to the model.
 18. The method according to claim15, wherein the step of selecting the first model further includes thesteps of: selecting a first set of coefficients to be applied to thefirst model for fitting the second dual-energy x-ray attenuationinformation with the first model; and, fitting the second dual-energyx-ray attenuation information with the first model optimizing the firstcoefficients; and, the step of selecting the second model furtherincludes the steps of: selecting a second set of coefficients to beapplied to the second model for fitting the second dual-energy x-rayattenuation information with the second model; and, fitting the seconddual-energy x-ray attenuation information with the second modeloptimizing the second set of coefficients.
 19. The method according toclaim 18, wherein the step of selecting the first model further includesthe steps of: selecting a first set of fitting constraints to be appliedto the first model for selecting the first set of coefficients; and,selecting the set of first coefficients by applying the first set offitting constraints to the first model; and, the step of selectingsecond the model further includes the steps of: selecting a second setof fitting constraints to be applied to the second model for selectingthe second set of coefficients; and, selecting the second set ofcoefficients by applying the second set of fitting constraints to thesecond model.
 20. The method according to claim 6, wherein thedual-energy x-ray attenuation information includes high-energy x-rayattenuation information and low-energy x-ray attenuation information andwherein the step of associating each of the first low-energy x-rayattenuation information and the first high-energy x-ray attenuationinformation with each of the first reference material path lengths andthe second reference material path lengths further comprises: defining afirst space wherein the first low-energy x-ray attenuation informationof the first reference material and the second reference materialdefines a first plane and first reference material path lengths andsecond reference material path lengths each define a first height overthe first plane; defining a second space wherein the first high-energyx-ray attenuation information of the first reference material and thesecond reference material defines a second plane and first referencematerial path lengths and second reference material path lengths eachdefine a second height over second the plane; and, representingcollectively the first reference material path lengths and the secondreference material path lengths using the model to define the firsthigh-energy direct attenuation surface and first low energy directattenuation surface.
 21. The method according to claim 10, wherein thedual-energy x-ray attenuation information includes high-energy x-rayattenuation information and low-energy x-ray attenuation information andwherein the associating step further comprises: defining a space whereinthe first reference material path lengths and the second referencematerial path lengths define a first plane and the first high-energyx-ray attenuation information and the first low-energy x-ray attenuationinformation each define a respective first and second height over thefirst plane and representing collectively the first high-energy x-rayattenuation information and the first low-energy x-ray attenuationinformation using the first model to define the first high-energy directattenuation surface and first low energy direct attenuation surface;and, defining an inverse space wherein the first low-energy x-rayattenuation information and the first high-energy x-ray attenuationinformation define a second plane and first reference material pathlengths and second reference material path lengths each define arespective third and fourth height over the second plane; and,representing collectively the first reference material path lengths andthe second reference material path lengths using the second model todefine first high-energy and first low-energy inverse attenuationsurfaces.
 22. The method according to claim 8, wherein the dual-energyx-ray attenuation information includes high-energy x-ray attenuationinformation and low-energy x-ray attenuation information and wherein thestep of associating each of the second low-energy x-ray attenuationinformation and the second high-energy x-ray attenuation informationwith each of the second reference material path lengths and thirdreference material path lengths further comprises: defining a firstspace wherein the second low-energy x-ray attenuation information of thesecond reference material and the third reference material defines afirst plane and second reference material path lengths and thirdreference material path lengths each define a first height over thefirst plane; defining a second space wherein the second high-energyx-ray attenuation information of the second reference material and thethird reference material defines a second plane and second referencematerial path lengths and third reference material path lengths eachdefine a second height over second the plane; and, representingcollectively the second reference material path lengths and the thirdreference material path lengths using the model to define the secondhigh-energy direct attenuation surface and second low energy directattenuation surface.
 23. The method according to claim 22, wherein theassociating step further comprises: defining a space wherein the secondreference material path lengths and the third reference material pathlengths define a first plane and the second high-energy x-rayattenuation information and the second low-energy x-ray attenuationinformation each define a respective first and second height over thefirst plane and representing collectively the second high-energy x-rayattenuation information and the second low-energy x-ray attenuationinformation using the first model to define the second high-energydirect attenuation surface and second low energy direct attenuationsurface; and, defining an inverse space wherein the second low-energyx-ray attenuation information and the second high-energy x-rayattenuation information define a second plane and second referencematerial path lengths and third reference material path lengths eachdefine a respective third and fourth height over the second plane; and,representing collectively the second reference material path lengths andthe third reference material path lengths using the second model todefine second high-energy and second low-energy inverse attenuationsurfaces.
 24. The method according to claim 1, wherein the step ofjoining the first the first dual-energy x-ray attenuation informationrange with the second dual-energy x-ray attenuation information rangefurther comprises the steps of: selecting a first model for expressingcollectively each of the first reference material path lengths and thesecond reference material path lengths as a function of the associatedfirst dual-energy x-ray attenuation information range; selecting a firstset of coefficients to be applied to the first model for fitting thefirst dual-energy x-ray attenuation information range with the firstmodel; selecting a second model for expressing collectively each of thesecond reference material path lengths and the third reference materialpath lengths as a function of the associated second dual-energy x-rayattenuation information range; selecting a second set of coefficients tobe applied to the second model for fitting the second dual-energy x-rayattenuation information range with the second model; weighting to a zerovalue the coefficients for fitting the dual-energy x-ray attenuationinformation of the first reference material to the first model to obtaina subset of coefficients for fitting respective dual-energy x-rayattenuation information of only the second reference material to eitherof the first model and the second model; and, fitting the first set ofcoefficients with the second set of coefficients using the subset ofcoefficients to join the first model and the second model to provide thethird dual-energy x-ray attenuation information range.
 25. A method forassigning an attribute to x-ray attenuation comprising: acquiring firstand second reference material equivalent path length informationassociated with a first range of dual-energy x-ray attenuationinformation by a first model for expressing collectively each of thefirst reference material path lengths and the second reference materialpath lengths as a function of the associated first range of dual-energyx-ray attenuation information, the first range of dual-energyattenuation information being fitted with the first model by a first setof coefficients; acquiring third reference material equivalent pathlength information associated with a second range of dual-energy x-rayattenuation information by a second model for expressing collectivelyeach of the third reference material equivalent path lengths as afunction of the associated second range of dual-energy attenuationinformation, the second range of dual-energy being fitted with thesecond model by a second set of coefficients, the third referencematerial having an effective atomic number greater than that of thesecond reference material; combining the first set of coefficients andthe second set of coefficients to provide a third set of coefficientsfor fitting the first and second range of dual-energy x-ray attenuationinformation with a third model for expressing collectively the first andthird reference material path lengths as a function of the fitted firstand second range of dual-energy x-ray attenuation information; and, forall points in the third model determine a volume fraction of one of thefirst and the third reference material which represents the secondreference material path lengths to identify where in the third modelpath lengths representing the second reference material are represented.26. The method as in claim 25, wherein the step of acquiring first andsecond reference material equivalent path length information associatedwith a first range of dual-energy x-ray attenuation information furthercomprises the steps of: scanning in an x-ray scanning device first andsecond reference materials each having known atomic composition, knowndimensions and known orientation in the x-ray scanning device, the x-rayscanning device emitting x-rays which pass through the first referencematerial with first reference material path lengths and through thesecond reference material with second reference material path lengths,the x-rays being detected by an array of detectors to provide firstdual-energy x-ray attenuation information for each of the first andsecond reference materials; associating each of the first dual-energyx-ray attenuation information with each of the first reference materialpath lengths and the second reference material path lengths; and,expressing collectively each of the first reference material pathlengths and the second reference material path lengths as a function ofthe associated first dual-energy x-ray attenuation information to definefirst dual-energy attenuation surfaces.
 27. The method as in claim 25,wherein the step of acquiring first and second reference materialequivalent path length information associated with a first range ofdual-energy x-ray attenuation information further comprises the stepsof: retrieving from lookup tables saved first and second referencematerial equivalent path lengths associated with the dual-energy x-rayattenuation information corresponding with the first dual-energyattenuation information range.
 28. The method as in claim 25, whereinthe step of acquiring third reference material equivalent path lengthinformation associated with a second range of dual-energy x-rayattenuation information further comprises the steps of: scanning in thex-ray scanning device the third reference material having known atomiccomposition, known dimensions and known orientation in the x-rayscanning device to provide second dual-energy x-ray attenuationinformation for the third reference material; associating each of thesecond dual-energy x-ray attenuation information with the thirdreference material path lengths; and, expressing collectively the thirdreference material path lengths as a function of the associateddual-energy x-ray attenuation information to define second dual-energyattenuation surfaces.
 29. The method as in claim 25, wherein the step ofacquiring third reference material equivalent path length informationassociated with a second range of dual-energy x-ray attenuationinformation further comprises the steps of: retrieving from lookuptables saved third reference material equivalent path lengths associatedwith the dual-energy x-ray attenuation information corresponding withthe second dual-energy attenuation information range.
 30. The methodaccording to claim 25, wherein the step of fitting the first model by afirst set of coefficients further includes the steps of: fitting thefirst range of dual-energy x-ray attenuation information with the firstmodel to optimize the first set of coefficients.
 31. The methodaccording to claim 25, wherein fitting the first range of dual-energyattenuation information with the first model by a first set ofcoefficients further includes the steps of: selecting a set of fittingconstraints to be applied to the first model for selecting the first setof coefficients; and, selecting the first set of coefficients byapplying the set of fitting constraints to the first model.
 32. Themethod according to claim 25, wherein the step of fitting the secondrange of dual-energy attenuation information with the second model by asecond set of coefficients further includes the steps of: fitting thesecond range of dual-energy x-ray attenuation information with thesecond model to optimize the second set of coefficients.
 33. The methodaccording to claim 25, wherein fitting the second range of dual-energyattenuation information with the second model by a second set ofcoefficients further includes the steps of: selecting a set of fittingconstraints to be applied to the second model for selecting the secondset of coefficients; and, selecting the second set of coefficients byapplying the set of fitting constraints to the second model.
 34. Themethod according to claim 25, wherein the dual-energy x-ray attenuationinformation includes high-energy x-ray attenuation information andlow-energy x-ray attenuation information and wherein associating thefirst range of dual-energy x-ray attenuation with each of the firstreference material path lengths and the second reference material pathlengths further comprises: defining a first space wherein the firstlow-energy x-ray attenuation information of the first reference materialand the second reference material defines a first plane and firstreference material path lengths and second reference material pathlengths each define a first height over the first plane; defining asecond space wherein the first high-energy x-ray attenuation informationof the first reference material and the second reference materialdefines a second plane and first reference material path lengths andsecond reference material path lengths each define a second height oversecond the plane; and, representing collectively the first referencematerial path lengths and the second reference material path lengthsusing the first model to define first dual-energy direct attenuationsurfaces.
 35. The method according to claim 25, wherein the dual-energyx-ray attenuation information includes high-energy x-ray attenuationinformation and low-energy x-ray attenuation information and whereinassociating the second range of dual-energy x-ray attenuationinformation with the third reference material path lengths furthercomprises: defining a first space wherein the second low-energy x-rayattenuation information of the third reference material defines a firstplane and the third reference material path lengths define a firstheight over the first plane; defining a second space wherein the secondhigh-energy x-ray attenuation information of the third referencematerial defines a second plane and the third reference material pathlengths define a second height over second the plane; and, representingcollectively the third reference material path lengths using the secondmodel to define second dual-energy direct attenuation surfaces.
 36. Themethod according to claim 25, wherein the dual-energy x-ray attenuationinformation includes high-energy x-ray attenuation information andlow-energy x-ray attenuation information and further comprising thesteps of: defining a space wherein the first reference material pathlengths and the third reference material path lengths define a firstplane and the first and second high-energy x-ray attenuation informationand the first and second low-energy x-ray attenuation information eachdefine a respective first and second height over the first plane and thethird model expresses collectively the first and third referencematerial path lengths as a function of the first and second low-energyx-ray attenuation and the first and second high-energy x-ray attenuationto define a third dual-energy direct attenuation surface; and, definingan inverse space wherein the first and second low-energy x-rayattenuation information and the first and second high-energy x-rayattenuation information define a second plane and first referencematerial path lengths and third reference material path lengths eachdefine a respective third and fourth height over the second plane; and,representing collectively the first reference material path lengths andthe third reference material path lengths using the third model todefine dual-energy inverse attenuation surfaces.
 37. A method forassigning an attribute to x-ray attenuation comprising: acquiring firstand second reference material equivalent path length informationassociated with a first range of dual-energy x-ray attenuationinformation by a model for expressing collectively each of the firstreference material path lengths and the second reference material pathlengths as a function of the associated first range of dual-energy x-rayattenuation information; selecting an extrapolation range of dual-energyx-ray attenuation information over which first and second referencematerial path lengths are to be associated with dual-energy x-rayattenuation information of a first imposed material having apredetermined minimum effective atomic number less than an effectiveatomic number of the first reference material and a second imposedmaterial having a predetermined maximum effective atomic number greaterthan an effective atomic number of the second reference material,wherein the first range is within the extrapolation range; selecting aset of fitting constraints for associating each of the first referencematerial path lengths and the second reference material path lengthsover the extrapolation range of dual-energy attenuation information todefine extrapolated first and second reference material equivalent pathlengths over the extrapolation range; and, applying the set of fittingconstraints to the model.
 38. The method as in claim 37, wherein thestep of acquiring first and second reference material equivalent pathlength information associated with a first range of dual-energy x-rayattenuation information further comprises the steps of: scanning in anx-ray scanning device first and second reference materials each havingknown atomic composition, known dimensions and known orientation in thex-ray scanning device, the x-ray scanning device emitting x-rays whichpass through the first reference material with first reference materialpath lengths and through the second reference material with secondreference material path lengths, the x-rays being detected by an arrayof detectors to provide first dual-energy x-ray attenuation informationfor each of the first and second reference materials; associating thefirst dual-energy x-ray attenuation information with each of the firstreference material path lengths and the second reference material pathlengths; and, using the model to express collectively each of the firstreference material path lengths and the second reference material pathlengths as a function of the associated first dual-energy x-rayattenuation information to define first dual-energy attenuationsurfaces.
 39. The method as in claim 37, wherein the step of acquiringfirst and second reference material equivalent path length informationassociated with a first range of dual-energy x-ray attenuationinformation further comprises the steps of: retrieving from lookuptables saved first and second reference material equivalent path lengthsassociated with the dual-energy x-ray attenuation informationcorresponding with the first range of dual-energy x-ray attenuationinformation.
 40. The method according to claim 37, wherein the applyingthe set of fitting constraints to the model further includes the stepof: selecting a set of coefficients to be applied to the model forfitting the dual-energy x-ray attenuation information of the first rangewith the model; and, fitting, using the set of fitting constraints, thedual-energy x-ray attenuation information of the extrapolation rangewith the model.
 41. The method according to claim 37, wherein thedual-energy x-ray attenuation information includes high-energy x-rayattenuation information and low-energy x-ray attenuation information andwherein associating each of the first and second reference material pathlengths with the first range of dual-energy x-ray attenuationinformation further comprises: defining a first space wherein thelow-energy x-ray attenuation information of the first reference materialand the second reference material defines a first plane and firstreference material path lengths and second reference material pathlengths each define a first height over the first plane; defining asecond space wherein the high-energy x-ray attenuation information ofthe first reference material and the second reference material defines asecond plane and first reference material path lengths and secondreference material path lengths each define a second height over secondthe plane; and, representing collectively the first reference materialpath lengths and the second reference material path lengths using thefirst model to define the dual-energy direct attenuation surfaces. 42.The method according to claim 37, wherein the dual-energy x-rayattenuation information includes high-energy x-ray attenuationinformation and low-energy x-ray attenuation information and wherein thestep of selecting a second model further comprises: defining a firstspace wherein the low-energy x-ray attenuation information of the firstimposed material and the second imposed material defines a first planeand first imposed material path lengths and second imposed material pathlengths each define a first height over the first plane; defining asecond space wherein the high-energy x-ray attenuation information ofthe first imposed material and the second imposed material defines asecond plane and first imposed material path lengths and second imposedmaterial path lengths each define a second height over second the plane;and, representing collectively the first imposed material path lengthsand the second imposed material path lengths using the second model todefine the extrapolated dual-energy direct attenuation surfaces.